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The volume of the given triangular pyramid is 16740.768 cubic feet.

In the given triangular pyramid, dimensions of rectangular base are length=33.2 feet and width=19.1 feet.

Height of the triangular pyramid is 26.4 feet.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, volume = 33.2×19.1×26.4

= 16740.768 cubic feet

Therefore, the volume of the given triangular pyramid is 16740.768 cubic feet.

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The option that represents the active voice is:

B: My friend invited his whole class to Saturday's soccer championship.

The active voice is one that asserts that the person or thing represented by the grammatical subject performs the action represented by the verb. The passive voice is one that makes the subject the person or thing acted on or affected by the action represented by the verb.

Looking at the given options and applying the definitions above, we can see that options A, C and D are passive voice because the subject is the recipient of the action.

Thus, the statement "My friend invited his whole class to Saturday's soccer championship." represents the active voice.

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The percent of the bags of chips weigh less than 176 grams is b 16%

From the question, we have the following parameters that can be used in our computation:

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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The composite shape is made up of different simpler shapes, the option that would make the complex shape is

D) 1 square and 2 trapeziums

Assuming the shape at the middle is of equal length and width, this describes a square and in this case the square is sitting on another shape and capped with another shape

Examining the image shows that the image at the base and on top are alike  and this shape is called trapezoid hence we can say that

The complex shape is made up of a  square and 2 trapeziums

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Answer: The Commutative law. It states a * b = b * a.

So, cba is the same as abc.

Step-by-step explanation:

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors.

Answer and Explanation:

The number property that allows the re-ordering of multiplication:

[tex]c\cdot b \cdot a[/tex]   to   [tex]a\cdot b\cdot c[/tex]

is the Commutative Property of Multiplication.

This property states that [tex]A\cdot B = B\cdot A[/tex].

We can test this property by plugging in numbers for A and B.

For example, if [tex]A = 2[/tex] and [tex]B=3[/tex]:

[tex]A\cdot B = 2 \cdot 3[/tex]

[tex]\implies \text{ this is an array of 2 rows and 3 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square \ \ \square\ \ \square \\ \square \ \ \square\ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]

__________________________________

[tex]B\cdot A = 3 \cdot 2[/tex]

[tex]\implies \text{ this is an array of 3 rows and 2 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square\ \ \square \\ \square\ \ \square \\ \square \ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}[/tex]

__________________________________

From this example, we can figure out that:

[tex]A \cdot B = B \cdot A = 6[/tex]

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

Answer: 28

Step-by-step explanation:

Triangle area formula is (bh)/2. Base is 7, height is 8. So those multiplied will be 56, and then divide by 2 to get 28. hope this helps!

Answer:

The answer is A

Step-by-step explanation:

The formula for annual percentage yield (APY) is:

APY = (1 + APR/n)^n - 1

where APR is the annual percentage rate, and n is the number of compounding periods per year.

For savings account A, APR = 2%, and it compounds interest quarterly, so n = 4. Therefore, its APY is:

APY_A = (1 + 0.02/4)^4 - 1 ≈ 0.0202 or 2.02%

For savings account B, APR = 2%, and it compounds interest annually, so n = 1. Therefore, its APY is:

APY_B = (1 + 0.02/1)^1 - 1 = 0.02 or 2%

Comparing the two APYs, we can see that savings account A has a slightly higher APY than savings account B. Therefore, the correct answer is:

A. Savings account A, because it has more compounding periods per year

The option that represents the ordering of the functions according to their average rates of change on the interval -1<=x<=1 goes least to greatest is f(x), h(x), g(x). Therefore, option A is the correct answer.

From the given graph, zeros are x=-3 and x=7.

(x+3)=0 and (x-7)=0

So, the equation is (x+3)(x-7)=0

x(x-7)+3(x-7)=0

x²-7x+3x-21=0

x²-4x-21=0

So, f(x)=x²-4x-21

From the table, the coordinates (-2, 27) and (-1, 18), we get

Slope(m) = (27-18)/(-1+2)

m=9

Substitute m=9 and (x, y)=(-2, 27) in y=mx+c, we get

27=9(-2)+c

c=27+18

c=45

So, the equation is g(x)=9x+45

Given that, h(x)=-x²+x+49

Therefore, option A is the correct answer.

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The general expression for the price elasticity of demand in terms of P is E = - (P / (15 - P)).

The value of P that makes the demand to be unit elastic would be 7.5.

The price elasticity of demand is given by the formula:

E = (%ΔQ / %ΔP) * (P/Q)

We can solve the demand equation for Q in terms of P as:

Q = 60 - 4P

Taking the derivative of Q with respect to P, we get:

dQ/dP = -4

We can now express the percentage change in Q as a function of the percentage change in P:

%ΔQ / %ΔP = (ΔQ / Q) / (ΔP / P) = (-4P/Q) / (P/Q) = -4

Substituting this expression into the formula for price elasticity of demand, we get:

To find the value of P for which demand is unit elastic, we need to set the absolute value of the price elasticity of demand equal to 1. So we have:

In other words, the value of P for which demand is unit elastic is 7.5.

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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4 1/4 inches

That number is the bottom side of the front, so it will also be the same side as the back.

The total area of the composite figure is 704 sq cm

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Area of Square + Area of Triangle

Using the above as a guide, we have the following equation

Area = 22 * 22 + 1/2 * 22 * (42 - 22)

Evaluate the products

Area = 484 + 220

Evaluate the sum

Area = 704

Hence. the total area of the figure is 704 sq cm

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Answer:

A

Step-by-step explanation:

Let's find the value of the function f(x) for x = √2. We'll substitute x by √2 in the equation:

f(√2) = 3(√2)² - 5√2√2 - 1

First, let's simplify the terms:

(√2)² = 2 ⇒ 3(2) = 6

5√2√2 = 5*2 = 10

Now, substitute these in the equation:

f(√2) = 6 - 10 - 1

f(√2) = -4 - 1

f(√2) = -5

Thus, the value of f(√2) is -5. The correct answer is (a).

Answer: 1/2

Step-by-step explanation:

Teddy can make 26 ornaments with 37/53 of clay left over

You should recall that Proportion is a mathematical comparison between two numbers, denoted using the symbol "::" or "=". It is an equation in which two ratios are set equal to each other

(20/1 ÷ 3/8)

Simplifying the fraction

20/1 * 8/3

Multiplying through to have

= 80/3

The correct solution is 26.66666

Covert the decimal to a mixed fraction to get 26 37/53

Therefore Teddy can make 26 ornaments with 37/53 of clay left over

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A. The mean of the sampling distribution is 0.85 (85%), and the standard error is approximately 0.085.

B. Since the sample size is 100, we can assume that the shape of the sampling distribution of the sample proportions is approximately normal.

C. The likelihood that the sample proportion of orders delivered on time will be less than 0.87 is approximately 59.07%.

D, The central 68.26% of the sample proportions are between 0.765 and 0.935.

To calculate the mean and standard error of the sampling distribution of sample proportions, we can use the following formulas:

Mean (μ) = p

= 85%

= 0.85

Standard Error (SE) = √[(p × (1 - p)) / n]

Where p is the population proportion (0.85) and n is the sample size (100).

Calculating the standard error:

SE = √[(0.85 × (1 - 0.85)) / 100]

SE = √[(0.7225) / 100]

SE = √[0.007225]

SE ≈ 0.085

The sampling distribution of sample proportions can be approximated by a normal distribution when the sample size is sufficiently large (central limit theorem).

To find the likelihood that the sample proportion of orders delivered on time will be less than 0.87, we need to calculate the z-score and refer to the standard normal distribution table.

First, we calculate the z-score:

z = (sample proportion - population proportion) / standard error

z = (0.87 - 0.85) / 0.085

z ≈ 0.02 / 0.085

z ≈ 0.235

Next, we look up the probability associated with the z-score of 0.235 in the standard normal distribution table.

The probability corresponds to the area to the left of the z-score.

Using the table, the probability is approximately 0.5907 or 59.07%.

The central 68.26% of the sample proportions are located within one standard deviation from the mean in a normal distribution.

To find the sample proportions that correspond to the central 68.26%, we can calculate the boundaries as follows:

Lower boundary: mean - standard deviation

Lower boundary = 0.85 - 0.085

Lower boundary = 0.765

Upper boundary: mean + standard deviation

Upper boundary = 0.85 + 0.085

Upper boundary = 0.935

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Answer:

8/3

Step-by-step explanation:

Slope of line =

[tex] \frac{y2 - y1}{x2 - x1} = \frac{4 - - 4}{0 - - 3} = \frac{4 + 4}{0 + 3} = \frac{8}{3} [/tex]

OR

Slope of line = vertical distance ÷ horizontal distance (vd/hd) = 8 ÷ 3 = 8/3

8/3 is an improper fraction so if you need it as a mixed number, it becomes 2⅔

A reflection and a dilation occurred to map △ABC to △A"B"C" (option C)

Geometry is all about understanding shapes and their various attributes, whether its symmetry, area, volume, or something else entirely. Two common operations that can significantly alter our perception of shapes are reflections and dilations.

A reflection involves transforming a shape by flipping it over an imaginary "mirror" - called the line of reflection - while preserving certain key features such as distance between points on either side of this mirror axis.

Alternatively dilation allows us to increase or decrease the size of shapes based on some scaling factor; this can also affect other key attributes like perimeter or surface area.

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Answer:

Linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:

d(t) = 1 + 3.5t

Step-by-step explanation:

To represent the total distance Janie ran and walked as a function of time, we need to consider two components: the distance she walks to the running track and the distance she runs on the track.

Distance walked to the running track: Janie walks 1 mile to reach the track. This distance remains constant regardless of the time she spends running.

Distance run on the track: Janie runs at a speed of 3.5 miles per hour. The distance she runs can be calculated by multiplying her running speed (3.5 miles/hour) by the time she spends running (t hours).

Therefore, the linear model representing the total distance she ran and walked, d, as a function of time, t, can be expressed as:

d(t) = 1 + 3.5t

Here, the constant term '1' represents the distance she walks to the track, and '3.5t' represents the distance she runs on the track, where t is the time she spends running in hours.

About 16% of the books have fewer than 150 pages

Given data ,

The numbers of pages in the books in a library follow a normal distribution

The mean number of pages is 180 and the standard deviation is 30 pages

Now , about 68% of the books will have a number of pages within one standard deviation of the mean, or between 150 and 210 pages

And , using a standard normal distribution table or a calculator that has a normal distribution function.

Using a standard normal distribution table, we find that the area to the left of -1 (which corresponds to a z-score of -1) is about 0.16

Hence , 16% of the books have fewer than 150 pages

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Answer:

Answer

Step-by-step explanation:

To model the variation in inches above and below the water level as a function of time in hours, we can use a cosine function.

First, we need to determine the amplitude and period of the function. The amplitude is half the difference between the high and low tides, which is (52 - 12)/2 = 20 inches. The period is the time it takes for one complete cycle, which is the time between consecutive high tides or low tides. In this case, the period is 6 hours, since high tide occurs every 6 hours.

The general form of a cosine function is:

y = A cos (Bx - C) + D

where A is the amplitude, B is the frequency (in radians per unit time), C is the phase shift (in radians), and D is the vertical shift.

Substituting the values we found, we get:

y = 20 cos ((2π/6)(x - 1.75)) + 32

where x is the time in hours since 9:15 a.m., and 1.75 is the phase shift (since high tide occurs at 3:00 p.m., which is 5 hours and 45 minutes after 9:15 a.m.). The vertical shift D is 32 inches, which is the average of the low and high tides.

Therefore, the cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m. is:

y = 20 cos ((2π/6)(x - 1.75)) + 32

The net gain of 4 points for these three days.

To find the net gain or loss of the stock for these three days, we need to add up the changes in value for each day.

On Monday,

the stock lost 7 1/8 points. This is the same as -7 1/8.

On Tuesday,

the stock lost another 1 7/8 points. This is the same as -1 7/8.

So the total change in value for Monday and Tuesday is:

= -7 1/8 - 1 7/8

= -9

On Wednesday,

the stock gained 13 points. This is the same as +13.

So the net change in value for the three days is:

= -9 + 13 = +4

Therefore, the net gain of 4 points for these three days.

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The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer:

Step-by-step explanation:

To find the unit price for each brand, we will divide the price of the box by the number of spoons in the box.

Unit price for the Brand A spoons:

$1.99 ÷ 25 = $0.0796 ≈ $0.08

Unit price for the Brand B spoons:

$3.89 ÷ 42 = $0.0926 ≈ $0.09

The better buy:

Brand A is the better buy, as its unit price is lower at $0.08 per spoon compared to Brand B's unit price of $0.09 per spoon.

Answer:

Approximate solution of the system is:

B. (5/2, -13/4)

Step-by-step explanation:

To approximate the solution of the given system of equations using the graph, we need to find the point where the two lines intersect. Let's analyze the equations and the graph to determine the approximate solution.

The given system of equations is:

-2x + 5y = 19 ...(1)

y = (-5/6)x - (1/6) ...(2)

Looking at equation (2), we can see that it represents a diagonal line with a negative slope, passing through the points (-5, 1) and (6, 6).

Now let's plot this line on the graph:

  |

6  |     x

  |

  |     x

5  |      x

  |

  |        x

4  |

  |

3  |

  |

2  |

  |

1  |  x

  |

0  |____________________

 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

The line rises from (-5, 1) to (6, 6).

Next, let's analyze equation (1), which can be rearranged as:

5y = 2x + 19

y = (2/5)x + (19/5)

Comparing equation (1) with equation (2), we can see that the slope of the line in equation (1) is positive, and it intersects the other line at a point. Therefore, we are looking for the point where the rising diagonal line intersects the line with a positive slope.

By visually examining the graph, we can approximate the intersection point to be around (5/2, -13/4).

Hence, the approximate solution of the system is:

B. (5/2, -13/4)

Answer:

x = 72 degrees

Step-by-step explanation:

By the Vertical Angles Theorem, the angle opposite the angle (let's call it angle z, the red text in the image I sent) with 108 degrees is also equal to 108 degrees.

By the Linear Pair Theorem, angle z degrees + angle x degrees = 180 degrees.

108 + x = 180, x = 72 degrees

The percentage of increase in sales from last month to this month is 9%.

Given,

Sales for last month = £180 000.

Sales for this month = £196 200.

To calculate the percentage increase, we must first find the difference in sales between the two months:-

Difference between the two months = £180,000 -  £196,200 = £16,200

Percentage of this difference = (16,200 ÷ 180,000) * 100 = 9

Thus, the percentage of increase is 9% from the last month to this month.

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