ABC forms a right-angled triangle
Let the distance between AB = x
Using Pythagoras theorem
Sin 30 = Opposite / Hypoteneuse
Sin 30 = 12 in/ x
However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.
Using Pythagoras' theorem, Sin 30 = 1/ 2
Substituting back into the equation, we get:
1/ 2 = 12 in / x
Cross multiplying, we get:
x = 24 in
Recall x = AB
AB = 24 inches
To remember the angles and their respective formula, use SOHCAHTOA
Where sin x = Opposite / Hypoteneuse
Cos x = Adjacent / Hypoteneuse
Tan x = Opposite / Adjacent
Solve for x. Round your answers to two decimal places.
2x2 + 7x = 3
Answer:
[tex]x\approx0.39,-3.89[/tex]
Step-by-step explanation:
[tex]\displaystyle 2x^2+7x=3\\2x^2+7x-3=0\\\\x=\frac{-7\pm\sqrt{7^2-4(2)(-3)}}{2(2)}\\\\x=\frac{-7\pm\sqrt{49+24}}{4}\\\\x=\frac{-7\pm\sqrt{73}}{4}\\\\x\approx0.39,-3.89[/tex]
Help Quickly! A truck needs 7 gallons of fuel to travel 56 miles. Can the truck travel 48 miles with 6 gallons of fuel? Explain.
Giving brainliest
Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.
Given that, a truck needs 7 gallons of fuel to travel 56 miles.
The truck travel 48 miles with 6 gallons of fuel.
Here, the proportion is
7:56::6:48
We know that, the proportion is product of extremes = product of means
7×48 = 56×6
336 = 336
Therefore, the correct answer is option B.
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4 - 32 x (-0.25)-12/ 1/3
Answer:
8x is your answer.
Step-by-step explanation:
The photo shows how it's solved.
Find the area of the following rectangle. a = 12 ft b = 14 ft A = ft 2
Answer:
The area of the rectangle is 168 ft².
Step-by-step explanation:
Formula: A = lw
where l and w are the length and width of the rectangle respectively.
We're given with the length and the width as
a = 12 ft
b = 14 ft
Let's solve for the area using the formula above.
A = lw
A = 12ft(14ft)
A = 168 ft²
b. Does there appear to be any relationship between these two variables?
a. colder average low-temperature seems to lead to higher amounts of snowfall
b. there is no relationship
c. colder average low-temperature seems to lead to lower amounts of snowfall
c. Based on the scatter diagram, comment on any data points that seem to be unusual.
an average snowfall of nearly 100 inches.
a. no city has
b. only one city has
c. two cities have
d. three cities have
e. four cities have
f. more than four cities have
1. There is no relationship
2. Two cities have an average snowfall of nearly 100 inches.
What is the scatter plot?
A scatter plot, also known as a scatter diagram or scatter graph, displays the relationship between two variables. It is particularly beneficial for identifying any patterns or trends in the data and showing how one variable might be related to another.
In a scatter plot, each data point is represented on the graph by a dot or marker. The horizontal axis (x-axis) is frequently used to represent the independent variable or predictor, while the vertical axis (y-axis) is frequently used to represent the dependent variable or reaction. Each dot's locations on the graph correspond to the values of the two variables for that particular data point.
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A sample of 22 observations selected from a normally distributed population produced a sample variance of 18 . a. To see if the population variance differs from 14 write the null and alternative hypotheses. b. Using �=.05α=.05, find the critical values of �2χ2. Display the chi-square distribution curve's rejection and nonrejection areas. c. Determine the test statistic �2χ2 value. d. Will you reject the null hypothesis presented in component an at a 5% significance level?
The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.
The null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): The population variance is equal to 14.
Alternative Hypothesis (Ha): The population variance differs from 14.
To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.
For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.
In this case, n = 22, so the degrees of freedom is 21.
Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.
The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.
To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.
The chi-square test statistic is calculated as:
χ2 = (n - 1) ×(sample variance) / (population variance)
Plugging in the values, we have:
χ2 = (22 - 1) × 18 / 14
=27
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helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer: $1.50 for every 1 pound
Step-by-step explanation:
If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.
how many inches is it from end to end on a bed that is 6 feet long? It is measured in the.
The calculated inches from end to end on the bed is 72 inches
How to determine the inches from end to end on the bedFrom the question, we have the following parameters that can be used in our computation:
Length = 6 feet long
By conversion of units, we have
1 feet = 12 inches
using the above as a guide, we have the following:
Length = 6 * 12 inches long
Evaluate the products
Length = 72 inches long
Hence, the inches from end to end on the bed is 72
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a shade of paint purple berry can be made by mixing red and blue paint in the ratio 5:2. Emma has 30 litres of red paint and 10 litres of blue paint.work out the maximum volume of purple berry that can be made
Answer:The max volume of Purple berry paint is 85
Step-by-step explanation:
Purple = Red + Blue
P = 5 : 2
Simplify 5 : 2 which is 2.5 : 1
P = 30L : 10L
P = (30 x 2.5 ) + (10 x 1)
P = 75 + 10
P = 85 L
Pls help me with this asap
Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.
Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.
Radius (r) = 8 cm / 2 = 4 cm
Height (h) = 19 cm
So, V1 = π(4 cm)²(19 cm)
≈ 3032.07 cm³
Container #2:
Radius (r) = 5 cm
Height (h) = 12 cm
Using the formula:
V2 = π(5 cm)²(12 cm)
≈ 942.48 cm³
Container #3:
Diameter (d) = 12 cm
Radius (r) = 12 cm / 2 = 6 cm
Height (h) = 10 cm
V3 = π(6 cm)²(10 cm)
≈ 1130.97 cm³
Now, Comparing the volumes:
V1 ≈ 3032 cm³
V2 ≈ 942 cm³
V3 ≈ 1131 cm³
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Need the answer ASAP
Answer: A. x=3 y= -1 z=4
Step-by-step explanation:
I plugged it into my graphing calculator.
>2nd Matrix
>Edit >A
>choose 3x3
>Enter all coefficients as they look
>2nd Matrix
>Edit >B
>Choose 3x1
>Enter answers as they look
Go to main page
[tex][A]^{-1} [B]\\[/tex]
Answers end up being 3, -1, 4
Given that tanx = 10 and sinx is negative, determine sin(2x), cos(2x), and tan(2x)
Sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.
How did we get the value?To find the values of sin(2x), cos(2x), and tan(2x) using the given information, use trigonometric identities to express them in terms of tan(x) and sin(x).
Given that tan(x) = 10 and sin(x) is negative. Since tan(x) = sin(x)/cos(x), find cos(x) using the given information.
Let's solve for cos(x) first:
tan(x) = sin(x)/cos(x)
10 = sin(x)/cos(x)
Now, let's find sin(x) using the given information that sin(x) is negative:
Since tan(x) = sin(x)/cos(x) and tan(x) = 10, substitute 10 for sin(x)/cos(x):
10 = sin(x)/cos(x)
Multiplying both sides by cos(x):
10 x cos(x) = sin(x)
Now, sin(x) = 10 x cos(x).
Since sin(x) is negative, conclude that cos(x) must be positive.
Now, let's use the double-angle identities to find sin(2x), cos(2x), and tan(2x):
sin(2x) = 2 x sin(x) x cos(x)
cos(2x) = cos²(x) - sin²(x)
tan(2x) = sin(2x) / cos(2x)
Substituting sin(x) = 10 x cos(x) into the above formulas, express sin(2x), cos(2x), and tan(2x) in terms of cos(x):
sin(2x) = 2 x (10 x cos(x)) x cos(x) = 20 x cos²(x)
cos(2x) = cos²(x) - (10 x cos(x))² = cos²(x) - 100 x cos²(x) = -99 x cos²(x)
tan(2x) = sin(2x) / cos(2x) = (20 x cos²(x)) / (-99 x cos²(x)) = -20/99
Therefore, sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.
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A 27 - foot ladder is leaning against the wall. If the top of the ladder touches 22.5 feet up the wall, what is the angle evaluation of the ladder
Answer:
Step-by-step explanation:
100 Points! Geometry question. Find each measure. Photo attached. Please show as much work as possible. Thank you!
Answer:
a. 73°
b. 98°
Step-by-step explanation:
In quadrilateral EFGH
∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
11x+8+8x+1=180°
19x+9=180°
19x=180=9
19x=171
x=171/19
x=9°
similarly,
∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
6y-4+5y-3=180°
11y-7=180°
11y=180°+7
11y=187°
y=187/11
y=17°
Now
a. m∡G=8x+1=8*9+1=73°
b. m∡H=6y-4=6*17-4=98°
100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!
The value of x is approximately 34.02.
Given that in a rectangle with length 31 and width is 14 and the diagonal length is x.
To find the value of x using the Pythagorean Theorem, we can consider the rectangle as a right triangle, where the length and width of the rectangle form the two sides of the triangle, and the diagonal length (x) is the hypotenuse.
According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the given data gives,
[tex]x^2 = length^2 + width^2[/tex]
Substituting the given values into the equation:
diagonal length [tex]x^2 = 31^2 + 14^2[/tex]
diagonal length [tex]x^2[/tex] = 961 + 196
diagonal length [tex]x^2[/tex] = 1157
To find x, we take the square root of both sides:
diagonal length x = [tex]\sqrt{1157}[/tex]
diagonal length x = 34.02
Therefore, the value of x is approximately 34.02.
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The cafeteria lunch menu lists:
Pizza Cheese, Sausage, Pepperoni
Dessert - Pudding or Cookie
Drink-Water, Milk, Soda
How many different lunch meals can you construct from these choices?
O 18
O
O 81
03
Answer: 18
Step-by-step explanation:
Multiply number of each item possible
3*2*3=18
Help Quickly! A truck needs 7 gallons of fuel to travel 56 miles. Can the truck travel 48 miles with 6 gallons of fuel? Explain.
Giving brainliest
Pick A, B, C, or D
Write the quadratic equation in standard form that corresponds to the graph shown below.
The quadratic equation in standard form that corresponds to the given graph is [tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
To determine the quadratic equation in standard form that corresponds to the given graph, we need to identify the key features of the parabola. From the graph, we can see that the parabola opens upwards and intersects the y-axis at the point (0, c). We can also observe that the vertex of the parabola lies at the point (h, k).
The standard form of a quadratic equation is given as follows:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h, k) represents the coordinates of the vertex, and 'a' is a constant that determines the shape and direction of the parabola.
Looking at the graph, we can determine the vertex by identifying the x-coordinate where the parabola reaches its highest or lowest point. Let's assume the vertex is located at the point (h, k).
From the graph, it appears that the vertex lies at (-2, 4). Therefore, we have h = -2 and k = 4.
Now we can rewrite the equation as:
[tex]f(x) = a(x + 2)^2 + 4[/tex]
Next, we need to determine the value of 'a'. To do this, we can use another point on the graph. Let's consider the point (1, 0).
Plugging in the coordinates (1, 0) into the equation, we get:
[tex]0 = a(1 + 2)^2 + 4[/tex]
0 = 9a + 4
9a = -4
a = -4/9
Now we have the value of 'a'. Substituting it back into the equation, we get:
[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
Thus, the quadratic equation in standard form that corresponds to the given graph is:
[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
38.9 in²
Step-by-step explanation:
You want the area of the composite figure that is an 8-inch square with a semicircle removed.
Semicircle areaThe missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...
A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²
Square areaThe area of the square without the semicircle removed is ...
A = s² = (8 in)² = 64 in²
Composite areaAfter removing the semicircle from the square, the remaining area is ...
A = square area - semicircle area
A = 64 in² -25.1 in² = 38.9 in²
The area of the figure is about 38.9 square inches.
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An oven used 7.31 units of electricity over
4 hours.
What is the rate of electricity usage for this
oven in units per hour?
Give your answer to 1 d.p.
The rate of electricity usage for the oven is 1.8275 units per hour.
What is the rate of electricity usage for the oven?The electricity consumption represents the amount of electrical energy that has been consumed over a specific time in units of Wh (or kWh),
To get rate of electricity usage for the oven in units per hour, we will divide the total electricity used by the number of hours.
Data:
Electricity used: 7.31 units
Time: 4 hours
Rate of electricity usage = Electricity used / Time
Rate of electricity usage = 7.31 units / 4 hours
Rate of electricity usage = 1.8275 units per hour.
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A stainless steel patio heater is a square pyramid. the length of one of the base is 23.8. The slant height of the pyramid is 89.3 in. What is the height of the pyramid?
To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.
Using the Pythagorean theorem:
s^2 = (b/2)^2 + h^2
We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.
Plugging in the values:
89.3^2 = (23.8/2)^2 + h^2
Simplifying:
h^2 = 89.3^2 - (23.8/2)^2
h^2 = 7950.49 - 141.64
h^2 = 7808.85
Taking the square root of both sides:
h = √7808.85
h ≈ 88.37
Therefore, the height of the square pyramid is approximately 88.37 inches.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022. Andre visited Dubai over winter break. He stood 1000 meters away from the building, looked up at a 39.62 degree angle using a laser rangefinder and spotted the top of the building.
Andre
If every floor is 5.079 meters tall, how many floors are there in the Buri Khalifa?
The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.
We can make use of the data given to determine the Burj Khalifa's floor count.
Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.
Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.
tan(39.62°) = h / d
h = d * tan(39.62°)
h = 1000 * tan(39.62°) ≈ 753.7 meters
So, as per this, Number of floors = h / floor height
Number of floors = 753.7 meters / 5.079 meters
Number of floors ≈ 148.4 floors or 148 floors.
Thus, 148 floors are there in Burj Khalifa.
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Can someone help me with 12 & 13. And show your work!
Answer:
please see answers below
Step-by-step explanation:
Volume of sphere = (4/3) X π X r ³
volume of hemisphere = (2/3)X π X r ³
12) volume of hemisphere = (2/3)X π X r ³
= (2/3) X π X (5)³
= (250/3)π
= 261.80 km³ to nearest hundredth
13) 18 foot is the diameter. radius = 1/2 X diameter = 9.
volume of hemisphere = (2/3)X π X r ³
= (2/3) X π X (9) ³
= 1526.81 ft³ to nearest hundredth
I NEED HELP WITH MATH STATISTICS
The limits for the 95% confidence interval are given as follows:
Lower limit: 0.65.Upper limit: 0.77.What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 225, \pi = \frac{159}{225} = 0.7067[/tex]
Then the lower bound of the interval is given as follows:
[tex]0.7067 - 1.96\sqrt{\frac{0.7067(0.2933)}{225}} = 0.65[/tex]
The upper bound of the interval is given as follows:
[tex]0.7067 + 1.96\sqrt{\frac{0.7067(0.2933)}{225}} = 0,77[/tex]
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8 minutes before 6=?
Answer:
5:52
Step-by-step explanation:
Answer: 5:52
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Answers following the rounding instructions: see below for details
BC = 5.1
m∠B = 23°
m∠V = 116°
Step-by-step explanation:
Givens:
AC = 3
AB = 7
m∠A = 41°
Unknowns:
BC = ?
m∠B = ?
m∠C = ?
Find side BC using the law of cosines: c² = a² + b² - 2ab cos(C)
a² = 3² + 7² - 2(3)(7)(cos41)
a = √9 + 49 - 42(cos41)
a = 5.128 ≈ 5.13
side BC = 5.13
Use the law of sines to find m∠B: sin(A) / a = sin(B) / b = sin(C) / c
m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°
Sum of interior angles of a triangle is 180, so now you can find m∠C:
m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°
Rounding side BC to nearest tenth: BC = 5.1
Rounding angles to nearest whole degree:
m∠B = 23°
m∠V = 116°
Question #3
Determine if the following scenario is best described as an observational study, survey, or experiment.
A researcher wants to determine the effects of eating a vegan diet on overall health. The researcher finds 200 individuals, where
of them have eaten vegan for the past five years and the other 100 have not eaten vegan for the past five years. The participants
each given a health assessment and the data is analyzed in order to draw conclusions about how eating vegan can affect one's
overall health.
Experimental Study
Observational study
Saved Survey
The type of sytudy that we have here is the observational study.
What is the observational study?
In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.
In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.
The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.
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Erica is 33 years old. She has $580 in a checking account, $3400 in a savings
account, $22,000 in a retirement account, and owns a car worth $7700. What
is the total value of her liquid assets?
A. $3400
B. $3980
C. $33,680
D. $29,700
The total value of her liquid assets would be = $3,980. That is option B.
What is a liquid asset?An asset is said to be a liquid asset because it can easily be converted into cash in a short period of time.
Examples of liquid assets include the following:
Cash in checking accountCash in savings accountTherefore, the total value of liquid assets = $580+$3400 = $3980
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
626.71 cm^2
Step-by-step explanation:
Area of figure = area of half circle + Area of half circle + area of a rectangle
here, diameter=15 cm
radius = 15/2=7.5 cm
length=30cm
breadth=15cm
Now
Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth
=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15
=626.71 cm^2
pls help me solve this asap
Answer:
150
Step-by-step explanation:
the formula for this is 2a squared + 4 a h
when we plug everything in we end up getting 2*3 squared + 4*3*11
and when solved it gets toy 150