The area of the base of a square pyramid is 64 in². The height of each triangular face of the pyramid is 6 in.

What is the surface area of the pyramid?

128 in²


144 in²


160 in²


256 in²

Answer: 0.9 or 9/10

Step-by-step explanation:

The question asks how many miles did Camila walk in all, so we have to add 1/2 mile and 2/5 of a mile.

1/2 + 2/5 = 9/10

Answer:

9/10 of a mile

Step-by-step explanation:

1/2 + 2/5

= 5/10 + 4/10

=9/10

The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]

To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.

To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.

Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.

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The quadrilateral given is a square and the measure of the angles as required are as follows;

It follows from the task content that the given quadrilateral is a square.

Recall, that the four interior angles of a square sum up to 360° in which case, each vertices is a right angle.

Additionally, the diagonals of a square intersect at a point to form right angle at the point.

Also, each diagonals is a bisector of the angles at the vertices.

Therefore, we have that;

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The x-intercept and y-intercept of the graph of -7x + 3y = 21 are -3 and 7 respectively.

The x-intercept of a graph is the point where a line crosses the x-axis, while the y-intercept of a graph is the point where a line crosses the y-axis.

Therefore, the x-intercept is the value of x when y = 0 while the y-intercept is the value of y when x = 0.

Hence, let's find the x and y-intercept of -7x + 3y = 21

x-intercept

-7x + 3(0) = 21

-7x = 21

x = 21 / -7

x = -3

Y-intercept

-7x + 3y = 21

-7(0) + 3y = 21

3y = 21

y = 21 / 3

y = 7

Therefore,

x-intercept = (-3, 0)

y -intercept = (0, 7)

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The  required value of the ∠DPE = 40°.

Angles that are vertically opposite to one another at a particular vertex are formed by two straight lines meeting. Angles that are vertically opposed to one another are identical. These are referred to as perpendicular angles at times.

Using vertically opposite angle, ∠GPE = 35° and ∠KPF are equal

Then,

∠GPE = ∠KPF = 35°

Then Sum of all angles on straight line is 180°

∠KPF + ∠FP + ∠DPE = 180°

35° + 105° + ∠DPE = 180°

∠DPE = 180° - 140°

∠DPE = 40°

Thus, required value of the ∠DPE = 40°.

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The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached

Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are

The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.

In the problem, the graph plotted is that of cosine function and the amplitude of is 8

The 5 points marked are

(-π/16, 0) - the first point

(0, 8) - showing the amplitude and 1/4 cycle

(π/16, 0) - 1/2 cycle

(-π/16, -8) - 3/4 cycle

(3π/16, 0) - one complete cycle

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The probability that a woman chosen at random from this population is more than 67 inches tall is approximately 0.1492 or 14.92%.

To find the probability that a woman chosen at random from this population is more than 67 inches tall, we need to calculate the z-score for this height and then find the corresponding probability from the standard normal distribution.

The z-score is calculated as:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.

In this case, x = 67, μ = 64.3, and σ = 2.6. Substituting these values into the formula, we get:

z = (67 - 64.3) / 2.6

= 1.04

Next, we look up the probability corresponding to a z-score of 1.04 in a standard normal distribution table or using a calculator. The probability of a z-score being less than 1.04 is 0.8508.

Since we are interested in the probability of a woman being more than 67 inches tall, we need to subtract this probability from 1:

P(x > 67) = 1 - P(z < 1.04)

= 1 - 0.8508

≈ 0.1492

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The number of feet away is the base of the ladder from the end of the slide, g, as shown is 3 ft.

The base of the ladder from the end of the slide forms a right triangle.

Hypotenuse² = opposite² + adjacent²

Hypotenuse = 5 ft

Opposite = 4 ft

Adjacent = g

So,

Hypotenuse² = opposite² + adjacent²

5² = 4² + g²

25 = 16 + g²

subtract 16 from both sides

25 - 16 = g²

9 = g²

find the square root of both sides

√9 = g

g = 3 ft

In conclusion, the base of the ladder is 3 ft away from the end of the slide.

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The value of x is equal to 4.8 units.

In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:

Volume = base area × height of the prism.

Assuming the variable x represent the length of one side of its base. Since the height of this triangular prism measures 11 units and its volume measures 130.9 cubic units, the value of x can be determined as follows;

Base area of triangle = 1/2 × x × 5

Base area of triangle = 5x/2 square units.

Volume of triangular prism = base area × height of the prism.

130.9 = 5x/2 × 11

130.9/11 = 5x/2

11.9 = 5x/2

5x = 23.8

x = 4.8 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

We can conclude that it is unlikely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1 because the sample mean of 24 is different from the population mean of 20.

To answer this question, we can use a t-test to determine if the sample mean of 24 is significantly different from the population mean of 20.

The t-test formula is:

t = (x' - μ) / (s / √(n))

Where x' is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the question, we get:

t = (24 - 20) / (4.1 / √(9)) = 2.93

To determine if this t-value is significant, we need to compare it to the critical t-value for a two-tailed test with 8 degrees of freedom (n-1). Using a t-table or calculator, we find the critical t-value to be approximately 2.31 at a 5% significance level.

Since our calculated t-value of 2.93 is greater than the critical t-value of 2.31, we can reject the null hypothesis that the sample mean is equal to the population mean.

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The equation of the line that passes through (6,6) and is parallel to 3x - 2y = 4 is y = (3/2)x - 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

To find the equation of the line passing through (6,6) that is parallel to 3x - 2y = 4.

We need to find the slope of the given line first.

3x - 2y = 4

-2y = -3x + 4

y = (3/2)x - 2

The slope of the given line is 3/2.

Since the line we want to find is parallel to this line, it will have the same slope.

Therefore, we can use the point-slope form of the equation of a line to write the equation:

y - y1 = m( x - x1 )

Plug in m = 3/2 and (x1,y1) : (6,6)

y - 6 = (3/2)(x - 6)

Simplifying:

y - 6 = (3/2)x - 9

y = (3/2)x - 3

Therefore, the equation of the parallel line is y = (3/2)x - 3.

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Answer:

1.45 pounds

Step-by-step explanation:

6.6 divided by 4

Using fraction, the total number of cupcakes is obtained to be 5.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.

Specifically, if x is the total number of cupcakes, then we can write -

4/x = 80/100

where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.

Solving for x, we get -

x = 4 / (80/100) = 5

So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.

Therefore, in total there are 5 cupcakes.

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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.

The transformed function is f(x)=(-2*((x+5)²)-3) and green is graph.

The vertical shift depends on the value of k. The vertical shift is described as follows:

g(x) = f (x) + k - The graph is shifted up k units.

g(x) = f (x) − k - The graph shifts down units.

we have,

f(x)=x²

reflected in the x-axis

f(x)=-(x)²

vertically stretched by a factor of 2

f(x)=2*x²

shifted five units to the left

f(x)=(x+5)²

shifted three units to dawn

f(x)=x²-3

we can write all together

f(x)=(-2*((x+5)²)-3)

graphing red original function green is transformed function.

the complete question is-

The graph of f(x) = x^2 is reflected in the x-axis, vertically stretched by a factor of 2, shifted five units to the left, and shifted three units down.

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Answer: 37.7mm

Step-by-step explanation:

c = 2πr

c = 2π(6)

c ≈ 37.7

The period of the Markov chain is 2.

The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:

 P(i,j)   State 0   State 1    State 0   0.5   0.5    State 1   0.3   0.7  


Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.

Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.

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Slope intercept form of the given equation is y=16/5x-16/5

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. where, m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, refers measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, the y-coordinate of the location where the line's graph crosses the y-axis.

16x-5y=16

Writing equation in slope intercept form

16-5y=16

-5y=16-16x

y=16/-5 +16/5x

y=16/5x-16/5.

hence, Slope intercept form of the given equation is y=16/5x-16/5

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The graph that would have x - intercepts if the functions are graphed on the xy- coordinate plane, is C) y = 3 sec x.

An x-intercept is a point where the graph intersects the x-axis, which means the value of y is 0 at that point.

We can analyze the functions randomly.

y = csc x + 3

The cosecant function is the reciprocal of the sine function, so csc x = 1 / sin x. For this function to have x-intercepts, we need 1 / sin x + 3 = 0. However, this equation cannot be satisfied since the minimum value of 1 / sin x + 3 is greater than 0. Therefore, there are no x-intercepts for this graph.

y = 3 sec x

The secant function is the reciprocal of the cosine function, so sec x = 1 / cos x. For this function to have x-intercepts, we need 3(1 / cos x) = 0. This equation can be satisfied when cos x = 0, which occurs at x = (2n + 1)π/2, where n is an integer. Therefore, this graph has x-intercepts.

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As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.

To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.

Next, let's count the number of ways to choose one student to wipe down the tables.

Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.

To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:

17 x 16 x 15 = 4,080

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As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.

To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.

Next, let's count the number of ways to choose one student to wipe down the tables.

Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.

To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:

17 x 16 x 15 = 4,080

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Answer:

To evaluate f(x)=1/2x-3 for each value of x, we substitute each value into the function and simplify:

(a) f(-8) = (1/2)(-8) - 3 = -4 - 3 = -7

(b) f(0) = (1/2)(0) - 3 = 0 - 3 = -3

(c) f(3) = (1/2)(3) - 3 = 1.5 - 3 = -1.5

(d) f(10) = (1/2)(10) - 3 = 5 - 3 = 2

Therefore, the values of the function for each value of x are:

(a) f(-8) = -7

(b) f(0) = -3

(c) f(3) = -1.5

(d) f(10) = 2

Based on a linear regression model, if the crime rate increases to 131.2 in year 11, the predicted patient load would be approximately 72.733, so the psychologist is likely to treat 72 phobic patients.

Based on the given information, the psychologist has used a linear regression model to predict the number of phobic patients based on the crime rate in New York City. The regression equation is:

Predicted patients = 1.229 + 0.545 * Crime rate

Here, 0.545 is the coefficient for the Crime Rate variable.

Using this equation, we can predict the number of phobic patients in year 11 when the crime rate is 131.2

Predicted patients = 1.229 + 0.545 * 131.2

Predicted patients = 72.733

Therefore, by using the linear regression model, we find that the psychologist is expected to treat approximately 72 phobic patients in year 11 if the crime rate in New York City increases to 131.2.

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--The given question is incomplete, the complete question is

"a new york city psychologist specializes in treating patients who are phobic and afraid to leave their homes. the following table indicates how many patients the psychologist has seen each year for the past ten years. it also indicates the robbery rate in new york city during the same year. using crime rate to predict patient load, if the crime rate increases to 131.2 in year 11, how many phobic patients will be treated?

Regression Statistics Multiple R 0.950511723 R Sqar 0.903472536 Adjusted R 0.891406603 Square Standard 3.5485219 Error Observations ANOVA 10 df MS F Significance 1 942.8639386 942.8639386 74.87797 2.4715E-05 Regression Residual Total 8 100.7360614 12.59200768 1043.6 Coefficients Standard tStat P-value Lower 95% Upper 95% Error Intercept 1.229061531 5.497668676 0.223560495 0.828702 -11.44858516 13.90670822 Crime Rate 0.545008057 0.0629833718.653205606 2.47E-05 0.399768144 0.69024797 RESIDUAL OUTPUT Observation Predicted Patients Standard Residuals 33.00303125 34.80155784 41.23265291 42.48617144 45.42921495 49.7347786 56.32937609 52.89582533 57.52839382 64.55899775 0.89579985 0.53848918 0.368442379 -0.444219566 1.622803022 1.573785026 1.097156702 0.330039979 0.140964015 1.063791424 10"

The ordered pair is the best approximation of the exact solution is (0.6, 1.9). The correct option is c.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

y = -2x + 3

y = 5x - 1

Equate the right sides of both equations:

-2x + 3 = 5x - 1,

-2x - 5x = -1 -3,

x = 4/7

then

y = -2 x 4/7 + 3 = 8/7 + 3 = 3x7-8 /7 = 13/7 = 1 x 5/7

4/7 = 0.6 and 1 x 5/7 is equal to the ordered pair (0.6, 1.9).

Therefore, the correct option is c, (0.6, 1.9).

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The question is incomplete. The full question is given below:

Which ordered pair is the best approximation of the exact solution?

Answer:

Answer is B The data is asymetrical.

Step-by-step explanation:

No, the given statement about the lab experiment is not reasonable.

If Max places 1.98 grams of powdered substance into each glass plate and he needs to place the substance into 3 glass plates, then the total amount of the powdered substance he needs is 1.98 x 3 = 5.94 grams. This is greater than the amount Max estimates to be in the container (4.5 grams).

Therefore, it is not reasonable to assume that there are only 4.5 grams of  the powdered substance in the container when Max needs to use more than that amount for his experiment.

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Complete Question:

In chemistry lab, there are 9.52 grams of powdered substance in a container. Max needs to place substance into each of 3 glass plates. The amount of powdered substance he places into each glass plate is 1.98 grams. Max estimates that there are 4.5 grams of the powdered substance in the container. Is the statement reasonable?

An exponential equation, y = (20) 3ᵗ, shows the number of infected people from an outbreak of whooping cough. The number of Infected people reach 1000 after 3.56 weeks.

We have an equation that shows the number of people infected from a whooping cough outbreak. This equation is y is equal to 20 times 3 to the power of t, i.e. y = (20) 3ᵗ -- (1)

where y--> number of infected people

t--> time in weeks

An exponential equation is an equation with exponents where either the exponent or part of the exponent is a variable. As we see 't' is variable so, eqution (1) is an exponential equation. We have to determine time in weeks when the number of infected people count reach 1,000. Substitute, y = 1000 in (1)

=> 1000 = (20)3ᵗ

Dividing by 20 both sides

=> 1000/20 = 3ᵗ

=> 50 = 3ᵗ

Taking natural logarithm both sides,

=> ln(50) = ln( 3ᵗ)

=> ln(50) = t ln(3)

=> t = ln(50)/ln(3)

=> t = 3.56

Hence, required value of t is 3.56 weeks.

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The quantity cosecant squared of theta minus 1 can be simplified as 1/(cosecθ)² - 1. So, the correct answer is -1/tanθ.

Cosecant, denoted as csc, is a trigonometric function that is the reciprocal of the sine function. It is the ratio of the side opposite the angle over the hypotenuse in a right triangle.

This can be further simplified by multiplying the numerator and denominator of the fraction by the cosecant of theta to get the expression 1 - cosec²θ/cosecθ.

Rearranging this expression gives -cosec²θ/cosecθ.

The cosecant of theta can be further simplified by using the identity cosecθ = 1/sinθ.

Substituting this into the expression gives -1/sin2θ.

The sine of theta can then be further simplified by using the identity

sinθ = 1/tanθ.

Substituting this into the expression gives -1/tan²θ.

Finally, using the identity tan²θ = tanθ/1 simplifies the expression to -1/tanθ.

Therefore, the correct answer is -1/tanθ.

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Question:

The expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?

A. 1

B. 0

C. -cotθ

D. -1/tanθ

1) The point is on the unit circle.

2) The point is not on the unit circle

3) cos(Θ) = 0.866

We know that all the points on the unit circle have a magnitude of 1, then we can write:

√[ (-0.5)² + (sin(4π/3)²) = 1

This means that the point is on the unit circle.

b) Now the point is (-0.5, sin(5π/6))

We need to do the same thing, this time we will get:

√[ (-0.5)² + (sin(5π/6)²) = 0.71

So this point is not on the number line.

c) Here we know that sin(Θ) = -0.5 and the angle is in the quadrant 4.

Then Θ = Asin(-0.5) = -30°

Remember that -30° is on the fourth quadrant, so this is correct, now the cosine of that is:

cos(-30°) = 0.866

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Answer:

Step-by-step explanation:

look get 8 then 7 then you get 5 and luh tyler.

Answer:

13 bags

Step-by-step explanation:

V = π(2^2)(1/2) = 2π = 6.28 cubic feet

6.28 ÷ .5 = 12.56

So Martin needs to buy at least 13 bags of sand.

The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.

A mathematical assertion that two expressions are equal is known as an equation. A typical equation has one or more variables, which are often denoted by letters and have a range of possible values. Equations are frequently used in a variety of fields to describe relationships between distinct numbers or to address issues. For instance, the equation x + 2 = 5 only has one variable, x. It denotes that the product of x and 2 equals 5.

given

We can represent 556 as a rectangle with length 556 and width 1, and 16 as a rectangle with length 16 and width 1 to calculate the quotient of 556 and 16 using an area model.

This is how it goes:

To start, we deduct 16 from 556 to obtain:

556 - 16 = 540

540 = 16 x 33 + 4

Finally, by multiplying the numerator and denominator of the fraction 33 4/16 by 4, we may express the quotient of 556 and 16 as a mixed number in the simplest form, which results in:

556 ÷ 16 = 33 4/16 = 33 1/4

The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.

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