Answer:
3(5)^6
Step-by-step explanation:
There is 6, 5's in the expression meaning our answer has to be 3(5)^6.
:)
Answer:
the answer for the question given above is equal to 46875
Two car services charge different rates. A charges .60 per mile plus 3.00initial charge B charges .75 per mile mile traveled . the situation is modeled bu this system where x is the number of miles traveled and y is the charge for that distance ,in cents. How many miles must each car travel for the charges to be equal and ehat is the charge for that distance
The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.
To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.
Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:
For car service A: y_A = 0.60x + 300 (in cents)
For car service B: y_B = 0.75x (in cents)
To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:
0.60x + 300 = 0.75x
Subtracting 0.60x from both sides:
300 = 0.15x
Dividing both sides by 0.15:
x = 300 / 0.15
x = 2000
Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:
y_A = 0.60(2000) + 300
y_A = 1200 + 300
y_A = 1500 cents or $15.00
So, when each car travels 2000 miles, the charges will be equal at $15.00.
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Derrick Rolls a die many times and Records the number of times he rolls a three arrange the following situations in order from the situation that gets the largest difference between relative frequency and actual probability to the situation that gives the smallest difference
The order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
To determine the order of situations from the largest difference between relative frequency and actual probability to the smallest difference, we need to consider the concept of relative frequency and actual probability.
Relative frequency refers to the observed proportion of an event occurring in an experiment or trial, while actual probability represents the theoretical or expected probability of that event occurring.
Situation 1: Derrick rolls the die 10 times.
In this situation, the relative frequency of rolling a three can vary, but with a limited number of trials, the relative frequency might not accurately reflect the actual probability. Therefore, the difference between relative frequency and actual probability is likely to be larger compared to situations with more trials.
Situation 2: Derrick rolls the die 100 times.
With a larger number of trials, the relative frequency is expected to converge towards the actual probability. The difference between relative frequency and actual probability would likely be smaller compared to the previous situation.
Situation 3: Derrick rolls the die 1,000 times.
Increasing the number of trials further enhances the convergence of relative frequency to the actual probability. The difference between relative frequency and actual probability would be smaller than in the previous two situations.
Situation 4: Derrick rolls the die 10,000 times.
With an even larger number of trials, the relative frequency becomes more reliable and closely approximates the actual probability. The difference between relative frequency and actual probability would be smaller compared to the previous situations.
Situation 5: Derrick rolls the die 1,000,000 times.
In this situation, the large number of trials greatly increases the reliability and accuracy of the relative frequency. The observed relative frequency is expected to be very close to the actual probability, resulting in the smallest difference between the two.
Therefore, the order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:
Situation 1: Derrick rolls the die 10 times.
Situation 2: Derrick rolls the die 100 times.
Situation 3: Derrick rolls the die 1,000 times.
Situation 4: Derrick rolls the die 10,000 times.
Situation 5: Derrick rolls the die 1,000,000 times.
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What is the exact length of HG in cms
The given triangle is a right angled triangle, therefore the rules of basic Trigonometry can be used here to find the solution.
Considering angle G, lets find sin 45°[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin(45 \degree) = \frac{opposite \:\: side}{hypotenuse} [/tex]
[ sin 45° = 1/√2 ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{ \sqrt{2} } = \frac{b}{x} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = b \sqrt{2} \: \: cm[/tex]
So, the side HG is b√2 cm long
From the observation deck of a skyscraper, Morgan measures a 67^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
The Horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
We can use trigonometry and the concept of angles of depression. We can consider the height of the observation deck as the opposite side and the horizontal distance to the ship as the adjacent side of a right triangle.
Given that the angle of depression is 67 degrees and the height of the observation deck is 955 feet, we want to find the horizontal distance (adjacent side).
Using the trigonometric function tangent, we can set up the following equation:
tan(67°) = opposite/adjacent
tan(67°) = 955/adjacent
To find the value of the adjacent side (horizontal distance), we can rearrange the equation:
adjacent = 955/tan(67°)
Using a calculator, we can evaluate the tangent of 67 degrees:
tan(67°) ≈ 2.3693
Now we can substitute this value into the equation:
adjacent = 955/2.3693
adjacent ≈ 403.81
Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.
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Find the values of x and y with the answers in simplest radical form
The values of x and y in simplest radical form are :
5) x = 3 and y = 3√3
6) x = 5√3 and y = 10√3
7) x = 21 and y = 14√3
Given are three right angled triangles, whose angles are 30° - 60° - 90°.
The measures of sides for a 30° - 60° - 90° triangle is in the ratio 1 :√3 :2.
That is if length of the shorter leg which is the side opposite to 30° is k, then the length of the longer leg, which is the side opposite 60° will be √3k and the length of the hypotenuse, which is the side opposite to 90° will be 2k.
5) Using the above fact, here,
2k = 6
⇒ k = 6/2 = 3
So, x = 3 and y = 3√3
6) √3 k = 15
k = 15 /√3 = 5√3
So, x = 5√3 and y = 2 × 5√3 = 10√3
7) k = 7√3
So, x = √3 × 7√3 = 21
y = 2 × 7√3 = 14√3
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Don't forget to show your work. Thank you!
The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
We know that, probability of an event
= Number of favourable outcomes/Total number of outcomes.
Here, area of a rectangle = Length × Breadth
= 15×8
= 120 square units
Area of a triangle = 1/2 × Base × Height
= 1/2 ×(√10²-6²)×6
= 0.5×8×6
= 24 square units
Area of a trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(5+7)×2
= 12 square units
Area of a square = side² = 2²
= 4 square units
(a) Probability of landing in trapezium or Square = 12/120 + 4/120
= 16/120
= 2/15
(b) Probability of landing inside the rectangle but outside the triangle = 16/120
= 2/15
Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
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An ethical hacker, also referred to as a white hat hacker, is an information security expert who systematically attempts to penetrate a computer system, network, application or other computing resource on behalf of its owners. The purpose of ethical hacking is to evaluate the security of and identify vulnerabilities in systems, networks or system infrastructure. It includes finding and attempting to exploit any vulnerabilities to determine whether unauthorized access or other malicious activities are possible.
An ethical hacker is required to randomly guess the correct pin code that consists of the number 0 through 9 that must be entered in the correct order to access a company system.
1. What is the probability that the ethical hacker will guess the pin code correctly on the first try?
2. There are many variations of this guess. Assuming the primary variation allows the ethical hacker to guess correctly if the four-digit in the number are selected in any order as long as they are the same four digits as set by the IT security of the company.
For example, if the ethical hacker picks four digits making the number 2376, then the he will guest it right if 2376, 3726, 6327, 7632, and so forth, are entered. Consider the following four different versions of his presumptions.
(a) All four digits are unique (e.g. 1234)
(b) Exactly one of the digits appears twice (e.g. 2334, 8185)
(c) Two digits each appear twice (e.g. 1212, 8855)
(d) One digit appears three times (e.g. 2226, 8188)
Find the probability that the ethical hacker will successfully guess the accurate pin code in the first try for each of these four situations.
Show the necessary steps and explanation for the four presumptions stated above.
Answer: What is the probability that the ethical hacker will guess the pin code correctly on the first try?
Since the pin code consists of 10 possible digits (0 through 9), the probability of guessing the correct pin code on the first try is 1 in 10. This is because there is only one correct pin code out of the 10 possible options.
Therefore, the probability is 1/10 or 0.1 (or 10%).
Calculating the probability for each of the four situations:
(a) All four digits are unique (e.g., 1234):
In this case, there are 10 options for the first digit, 9 options for the second digit (since it can't be the same as the first), 8 options for the third digit, and 7 options for the fourth digit. The total number of possible combinations is given by:
10 × 9 × 8 × 7 = 5040
So, there are 5040 possible four-digit combinations when all digits are unique.
The probability of guessing the correct pin code on the first try in this situation is 1 in 5040, or 1/5040.
(b) Exactly one of the digits appears twice (e.g., 2334, 8185):
In this case, we have two scenarios to consider:
Scenario 1: The repeated digit is the first digit:
The first digit can be chosen in 10 ways, the second digit (repeated) can be chosen in 9 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:
10 × 9 × 8 × 7 = 5040
Scenario 2: The repeated digit is not the first digit:
The first digit can be chosen in 9 ways (excluding the repeated digit), the repeated digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:
9 × 10 × 8 × 7 = 5040
Combining both scenarios, we get a total of 2 × 5040 = 10080 possible combinations when exactly one of the digits appears twice.
The probability of guessing the correct pin code on the first try in this situation is 1 in 10080, or 1/10080.
(c) Two digits each appear twice (e.g., 1212, 8855):
In this case, there are two scenarios to consider:
Scenario 1: The two pairs of digits are different:
The first pair of digits can be chosen in 10 ways, the second pair of digits can be chosen in 9 ways, and the order of the pairs can be switched. So, the total number of possible combinations is:
10 × 9 × 2 = 180
Scenario 2: The two pairs of digits are the same:
The pair of digits can be chosen in 10 ways, and the order of the digits can be switched. So, the total number of possible combinations is:
10 × 1 = 10
Combining both scenarios, we get a total of 180 + 10 = 190 possible combinations when two digits each appear twice.
The probability of guessing the correct pin code on the first try in this situation is 1 in 190, or 1/190.
(d) One digit appears three times (e.g., 2226, 8188):
In this case, there are two scenarios to consider:
Scenario 1: The repeated digit is the first digit:
The first digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 9 and 8 ways, respectively. So, the total number of possible combinations is:
10 × 9 × 8 = 720
Scenario 2: The repeated digit is not the first digit:
The first digit can be chosen in 9 ways (excluding the repeated digit), and the repeated digit can be chosen in 10 ways. The remaining distinct digit can be chosen in 8 ways. So, the total number of possible combinations is:
9 × 10 × 8 = 720
Combining both scenarios, we get a total of 2 × 720 = 1440 possible combinations when one digit appears three times.
The probability of guessing the correct pin code on the first try in this situation is 1 in 1440, or 1/1440.
To summarize, the probabilities for each of the four situations are:
(a) All four digits are unique: 1/5040
(b) Exactly one of the digits appears twice: 1/10080
(c) Two digits each appear twice: 1/190
(d) One digit appears three times: 1/1440
Question Number 7 of 10 - 8th Grade Math
Which graph shows only a translation?
The graph that shows only a translation is (c)
How to determine the graph that shows only a translation?From the question, we have the following parameters that can be used in our computation:
The list of options
The general rule of translation it that
The image and the preimage have the same orientationThe image and the preimage have the same side lengthsThe image and the preimage have the same angle measuresUsing the above as a guide, we have the following:
the graph that shows only a translation is (c)
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Please help. Any unnecessary answers will be reported. Show your work.
King Arthur's Sword has a blade that is made of a regular hexagon and a regular pentagon. What is the amplitude of the tip of King Arthur's Sword?
Answer: Amplitude is 108 degrees
Step-by-step explanation:
To determine the amplitude of the tip of King Arthur's Sword, we need to understand the shape of the sword's blade, which consists of a regular hexagon and a regular pentagon.
A regular hexagon has six equal sides and six equal angles, each measuring 120 degrees. The regular pentagon, on the other hand, has five equal sides and five equal angles, each measuring 108 degrees.
Since the tip of the sword is formed by the meeting point of the hexagon and pentagon, it will be at the apex of the pentagon. The apex of the pentagon will have an angle of 108 degrees.
I hope this helps!!!
the next 3 terms of 10,13,17,238
Need help with proofs, anyone know how?
Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.
Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;
MS ≅ QSNS ≅ RSMN ≅ QN ∠NMS and ∠NQSΔMNS ≅ ΔQNSRead more on perpendicular bisectors here: brainly.com/question/19154899
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Complete Question:
The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS
We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.
NS and NS
NS and RS
MS and RS
MS and QS
Cylindrical solid has a circumference of 132cm,height is 30cm.what is the area of the solid
Step-by-step explanation:
Cylinder LATERAL S.A. = circ X Height = 132 cm X 30 cm = 3960 cm^2
PLUS the two ends = two X pi r^2
the circumference = pi * d = 132 cm
then diameter = 132 / pi then radius = 1/2 132 / pi = 66/ pi
so end areas : two * pi (66/ pi)^2 = 2773.1
TOTAL = 3960 + 2773.1 = 6733.1 cm^2
You are the architect for Pharaoh Khufu. He wants you to construct a square pyramid with a height of 100 m but you only have an limestone to fill a volume of 2,000,000 m³. How long should the sides of the square base be? Round your answer to the nearest hundredth.
The length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.
To calculate the length of the sides of the square base of the pyramid, we can use the formula for the volume of a square pyramid:
V = (1/3) * (side length)^2 * height
Given that the volume of the pyramid is 2,000,000 m³ and the height is 100 m, we can substitute these values into the formula:
2,000,000 = (1/3) * (side length)^2 * 100
To isolate the side length, we can rearrange the equation:
(side length)^2 = (2,000,000 * 3) / 100
(side length)^2 = 60,000
Taking the square root of both sides, we find:
side length ≈ √60,000
side length ≈ 244.95
Therefore, the length of each side of the square base should be approximately 244.95 meters when rounded to the nearest hundredth.
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line p is parallel to line q and both these lines are intersected by transversal t show workkkkkk
The value of x is equal to 10 degrees.
What is the Alternate Interior Angles Theorem?In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent:
By applying the alternate interior angles theorem to parallel lines p and q, we have the following congruent angles:
(5x - 65) = (x - 25)
5x - x = 65 - 25
4x = 40
x = 40/4
x = 10 degrees.
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Help with this question pls?
The image of point A after the reflection is A'(3, -4).
The image of point B after the reflection is B'(2, -3).
To reflect a point in the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate.
For point A(3, 4):
After reflecting point A in the x-axis, the y-coordinate remains the same (4), and the sign of the x-coordinate changes.
Therefore, the image of point A after the reflection is A'(3, -4).
To reflect a point in the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
For point B(-2, -3):
After reflecting point B in the y-axis, the x-coordinate remains the same (-2), and the sign of the y-coordinate changes.
Therefore, the image of point B after the reflection is B'(2, -3).
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4)Does this shape belong in a group of shapes that have more than one pair of
perpendicular sides?
Use the drop-down menus to explain your answer.
4) Click the arrows to choose an answer from each menu.
The number of right angles in this shape is Choose....
meet at a right angle is Choose....
perpendicular sides in this shape. This shape
shapes that have more than one pair of perpendicular sides.
. Each pair of sides that
▾ of
in a group of
.There Choose...
Choose...
No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.
Does the shape have > one pair of perpendicular sides?In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.
A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.
If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.
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Given below are lease terms at the local dealership. What is the total cash due at signing?
Terms:
Length of lease: 30 months
MSRP of the car $15,500
• Purchase value of the car after lease: $9900
Down payment $2500
Monthly payment $425
-Security deposit $375
Acustion fee $500
A. 375
B. 3375
C. 3800 (✅️)
D. 3400
Can someone help me with 12 & 13.
a) The volume of the hemisphere is V₁ = 261.80 km³
b) The volume of the hemisphere is V₂ = 1,526.81 feet³
Given data ,
a)
Let the volume of the hemisphere be represented as V₁
where the radius of the hemisphere is r₁ = 5 km
And , volume of hemisphere is V = ( 2/3 )πr³
On simplifying , we get
V₁ = ( 2/3 )π ( 5 )³
V₁ = 261.80 km³
b)
Let the volume of the hemisphere be represented as V₂
The diameter of the hemisphere = 18 feet
where the radius of the hemisphere is r₁ = 9 feet
And , volume of hemisphere is V = ( 2/3 )πr³
On simplifying , we get
V₂ = ( 2/3 )π ( 9 )³
V₂ = 1,526.81 feet³
Hence , the volume of the hemisphere is solved
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100 Points! Geometry question. Photo attached. Determine whether each pair or figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. Please show as much work as possible. Thank you!
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruent.
• Scale factor 1: 2.5
How to identify the similarity statement?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The pair of figures are similar because:
• Both figures are parallelograms
• All sides are congruent
• Angles W and Y are congruent with angles P and R
• Angles X and Z are congruent with angles S and Q
• Scale factor 1 : 2.5
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I need help bro how do you find the median, perp bisector, altitude, and angle bisector of a triangle? I need to know this for my final
You can determine the median of a triangle by looking out for the point that is 2/3 of the distance tht connects from the vertices, to midpoint and oposite sides.
The perpendicular bisector is determined by measuring the point that is equidistant from the segment.
How to find the altitude and angle bisectorThe altitude of a triangle can be found by measiring the height of the triangle's extension that could be inside or outside the triangle. In obtsue triangles, this altitude is commonly found outside the triangle.
Also, the angle bisector of a triangle is the point that is equidistant from the angles sides. These descriptions can help in analyzing a trinagle.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The length of y in the right triangle is 15 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sum of angles in a triangle is 180 degrees.
The side y in the triangle XYZ can be found using trigonometric ratios as follows:
Therefore,
sin 45 = opposite / hypotenuse
opposite sides = y
hypotenuse side = 15√2
sin 45 = y / 15√2
cross multiply
y = 15√2 × sin 45
y = 15√2 × 1 / √2
y = 15 units
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7.5, 8.5, 14.5 are these can form a triangle?
No, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.
To form a triangle considering three lengths of sides, the sum of the lengths of any two sides must be greater than the length of the third side.
Checking the above condition
1. The sum of 7.5,8.5 is 16, which is greater than 14.5. So, the condition is satisfied.
2. The sum of 7.5, 14.5 is 22, which is greater than 8.5. So, the condition is satisfied.
3. The sum of 8.5 and 14.5 is 23, which is less than 7.5. The condition is not satisfied.
Since the sum of the two shorter sides 8.5 and 14.5 is not greater than the longest side 7.5 these three sides with given lengths cannot form a triangle.
Therefore, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.
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WILL GIVE BRAINLIEST TO CORRECT ANSWER!!!
This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
X =
The value of x for the second triangle if it is the reduction of the first drawing is 6.3 feet.
Given two triangles.
Also given that, the scale drawings given are the reduction of the figure.
Most probably, the second triangle must be formed after a reduction with a scale factor of k.
Let k be the required scale factor.
The value of k can be found by taking the ratio of the corresponding sides.
k = 5.2 / 10.4
= 0.5
So all the corresponding sides will be half of the first triangle.
x = 0.5 × 12.6
= 6.3 feet
Hence the value of x is 6.3 feet.
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Molly used 192 beads to make a necklace AND a bracelet. It takes 5 times as many beads to make a necklace as it does a bracelet. How many beads are used to make the necklace?
Examining the word problem we can say that, Molly used 160 beads to make the necklace.
How to find the number of beadsLet's assume the number of beads used to make the bracelet is x.
We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,
x + 5x = 192
6x = 192
solve for x
x = 192 / 6
x = 32
Molly used 32 beads to make the bracelet.
number of beads used to make the necklace
Number of beads used for the necklace = 5 * 32
Number of beads used for the necklace = 160
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The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically?
x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
f(x), because it grows faster than g(x)
g(x), because it will not intersect f(x)
g(x), because it grows slower than f(x)
f(x), because it grows slower than g(x)
f(x) is the quadratic function.
g(x) is tripling its output for each 1-unit increase in x and g(x) = 3^x.
A quadratic function always grows more slowly than an exponential function.
So the best answer is:
f(x), because it grows slower than g(x)
a. Prices at Store A are 21% higher than at Store B
i. If the price at store A was $583, what was the price at store B?
ii. If the price at store B was $1200, what was the price at store A?
b. If there were 11,000 members in 2020 and 12,500 in 2021, what was the percent increase?
The answers are given as:
Ai. The price at Store B would be $583 / 1.21 = $481.82
ii. The price at Store A would be $1200 * 1.21 = $1452.
b. The percent increase in membership from 2020 to 2021 is 13.64%
How to solveA.
i. If the price at Store A was $583, the price at Store B would be $583 / 1.21 = $481.82 (approximately).
ii. If the price at Store B was $1200, the price at Store A would be $1200 * 1.21 = $1452.
b. The percent increase in membership from 2020 to 2021 is ((12,500 - 11,000) / 11,000) * 100 = 13.64% (approximately).
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Can someone help me with 12 & 13.
Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
12) Volume of semi - sphere = 261.67 km³
13) Volume of semi - sphere = 8574.29 feet³
We have to given that;
12) Radius of sphere = 5 km
13) Radius of sphere = 16 feet
Since, We know that;
Volume of sphere = 4/3 πr³
Hence, We get;
Volume of semi - sphere = 2/3πr³
12) Here, Radius of sphere = 5 km
Volume of semi - sphere = 2/3πr³
Volume of semi - sphere = 2/3 × 3.14 × 5³
Volume of semi - sphere = 261.67 km³
13) Here, Radius of sphere = 16 feet
Volume of semi - sphere = 2/3πr³
Volume of semi - sphere = 2/3 × 3.14 × 16³
Volume of semi - sphere = 8574.29 feet³
Thus, We get;
12) Volume of semi - sphere = 261.67 km³
13) Volume of semi - sphere = 8574.29 feet³
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45 points PLEASE HELP
The total number of each type of ball:
Football: Given as 8
Basketball: 18
Baseball: 40
Softball: 15
For basketball:
2 + 2(8) = 18
First, we evaluate the expression inside the parentheses: 2(8) = 16
Then, we add 2 to the result: 16 + 2 = 18
So, the total number of basketballs is 18.
For baseball:
5(8) = 40
We simply multiply 5 by 8 to get the total number of baseballs, which is 40.
For softball:
6 + 1/2(18) = 24
First, we evaluate the expression inside the parentheses: 1/2(18) = 9
Then, we add 6 to the result: 9 + 6 = 15
So, the total number of softballs is 15.
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Multiplying polynomials (7x - 5)(6x - 4)
The product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.
First, distribute the first term of the first polynomial (7x) to each term in the second polynomial (6x - 4):
7x × 6x = 42x²
7x × (-4) = -28x
Next, distribute the second term of the first polynomial (-5) to each term in the second polynomial (6x - 4):
-5 × 6x = -30x
-5 × (-4) = 20
Now, combine the like terms:
42x² - 28x - 30x + 20
Simplify the expression:
42x² - 58x + 20
Therefore, the product of (7x - 5)(6x - 4) is 42x^2 - 58x + 20.
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A refrigerator and 2 fans cost $1219. 2 refrigerators and 3 fans cost $2155. Find the cost of 1 refrigerator.
Answer:
$653
Step-by-step explanation:
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Let's use x to represent the cost of one refrigerator and y to represent the cost of one fan.
The equations become:
Equation 1: x + 2y = 1219
Equation 2: 2x + 3y = 2155
Using the same substitution method:
From Equation 1, we have:
x = 1219 - 2y
Substitute this expression for x in Equation 2:
2(1219 - 2y) + 3y = 2155
Simplify the equation:
2438 - 4y + 3y = 2155
-y = 2155 - 2438
-y = -283
===> y = 283
Now substitute the value of y back into Equation 1 to find x:
===> x + 2(283) = 1219
===> x + 566 = 1219
===> x = 1219 - 566
===> x = 653
Therefore, the cost of one refrigerator is $653.