Three oblique pyramids have the same regular square base. Which one has a volume of 15 cubic units if the area of the bases are all 15 square units?
An oblique triangular pyramid is shown. The slant height is 5, the vertical height is 4, and the base of the triangle formed is 3.

An oblique triangular pyramid is shown. The slant height is 5, the vertical height is 3, and the base of the triangle formed is 4.

An oblique triangular pyramid is shown. The slant height is 15, the vertical height is 12, and the base of the triangle formed is 9.

The requried, factored form of 6x²+7x-10 is (6x - 5)(x + 2).

To factor 6x²+7x-10, we need to find two numbers whose product is -60 (the product of the coefficient of x² and the constant term) and whose sum is 7 (the coefficient of x).

Now, we can factor by grouping:

(6x² + 12x) - (5x + 10)

6x(x + 2) - 5(x + 2)

(6x - 5)(x + 2)

Therefore, the factored form of 6x²+7x-10 is (6x - 5)(x + 2).

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The best answer is It is not possible to save any money this month without having a negative actual net income.

This is because saving money means spending less than you earn.

If the actual net income is already zero or positive, there is no room to save without spending more than the income, which would result in a negative actual net income.

Therefore, option B, C, and D are incorrect as they all suggest that it is possible to save money without having a negative actual net income, which is not possible.

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The minimum side length of the square piece of plywood is approximately 88.83 cm.

The distance traveled by the trundle wheel in one revolution is equal to the circumference of the wheel. Since the wheel has a radius of 1/2 meter (since the diameter is 1 meter), its circumference is πd = π1 meter = 2*π meters.

Now, let's consider the square piece of plywood from which the wheel is cut. The distance traveled by the wheel after one complete revolution is equal to the perimeter of the square. If we let x be the side length of the square, then its perimeter is 4x.

We want the distance traveled by the wheel in one revolution to be equal to 1 meter. Therefore, we set the circumference of the wheel equal to the perimeter of the square and solve for x,

2*π = 4x

x = (2*π)/4

x = π/2

Converting to centimeters, we get,

x = (π/2)*100 cm

x = 157.08 cm

Therefore, the minimum side length of the square piece of plywood is approximately 157.08 cm. However, we need to round our answer to two decimal places. Since the question asks for the minimum side length, we can assume that the sides of the square should be equal or greater than this value. Rounding to two decimal places, we get,

x ≈ 88.83 cm

Therefore, the minimum side length of the square piece of plywood is approximately 88.83 cm.

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The unit vector in the direction of v = 3i - 5j is (3√(34)i - 5√(34)j) / 34.

To find the unit vector in the direction of the given vector, we first need to find the magnitude of the vector v. The magnitude of a vector is the length or size of the vector and is calculated using the Pythagorean theorem:

|v| = √((3)² + (-5)²)

|v| = √(9 + 25)

|v| = √(34)

Now, we can find the unit vector u in the direction of v by dividing v by its magnitude:

u = v / |v|

u = (3i - 5j) / √(34)

This is the unit vector that has the same direction as v. To simplify the answer, we can rationalize the denominator by multiplying the numerator and denominator by √(34):

u = (3i - 5j) / √(34) * √(34) / √(34)

u = (3√(34)i - 5√(34)j) / 34

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The volume of the solid is V = 250/3 cubic units for the equation y = √(25 - x²)

The equation of the semicircle is given by y = √(25 - x²) where -5 ≤ x ≤ 5. We can also rewrite it as x² + y² = 25.

Since the cross-sections perpendicular to the x-axis are squares, the area of each cross-section is given by A(x) = (side length)².

We need to find an expression for the side length in terms of x.

Let the side length of a cross-section at x be s.

Since the cross-section is a square, we have s = h(x) for some function h. The height of the cross-section is given by h(x) = 2y = 2√(25 - x²). Therefore, the area of each cross-section is A(x) = (2√(25 - x²))²

= 4(25 - x²).

To find the volume of the solid, we integrate the area function A(x) over the interval [-5, 5]:

V = ∫A(x) dx

= ∫4(25 - x²) dx [from -5 to 5]

= 250/3

Therefore, the volume of the solid is V = 250/3 cubic units.

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Answer:

If we denote the unknown number as "x", then the expression representing "9 less than the unknown number" would be:

x - 9

The value of the k is; 1/12

The proportion is given by the expression;

y = kxz

Given the values;

y=6 when x=4 and z=12

To find the constant, k;

6 = k*4*12

6= 48k

k = 4/48

k = 1/12

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The voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it is 200 volts.

Given that we need to find the voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it,

Using the Ohm's law,

V = IR

V = 20 x 10

V = 200 Volts

Hence the voltage across a resistor with a resistance of 10Ω that has a current of 20A going through it is 200 volts.

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Answer:

$155

Step-by-step explanation:

15 x 7 + 50 = 155

Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

We will use a two-sample t-test.

Unsuccessful applicants (Group 1):

n1 = 23

Mean1 (x1) = 41.6

Standard deviation1 (s1) = 14.5

Successful applicants (Group 2):

n2 = 25

Mean2 (x2) = 39.7

Standard deviation2 (s2) = 5.4

Claim: μ1 > μ2

Opposite: μ1 ≤ μ2

In order to compare the means of two independent samples, a two-sample t-test is used.

The initial step involves calculating both the pooled variance (Sp^2) and standard error (SE).

To calculate Sp^2, use the formula ((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2),

As per our specific data set regarding sample one consisting of 22 values with an average age of 41.6 years old, and sample two having 24 values averaging at 39.7 years old, we derived a pooled variance value of 120.569.

After that, employ the equation SE = √((Sp^2/n1) + (Sp^2/n2)), which yields a value of 3.685 via inputting the aforementioned values.

Using these results enables us to take the difference of the two averages divided by SE in a simplified manner giving a t-score equal to .516.

In light of this test possessing a significance level of 0.01 and utilizing only one tail, a comparison of the calculated t-score to the t-distribution table must occur; using a critical t-value of 2.410 wherein the degrees of freedom are required to be 46.

Our calculation led to a P-value of .516, exceeding the predefined significance level of 0.01 which thereby disproves any evidence indicating individuals whose applications were unsuccessful came from a group whose members had higher mean ages than those who were successful.

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The venn diagram represents C'  ∩ (A ∪ B).

First, the region of C is whole shaded.

Now, C is having a common part in A and B then we need the intersecting part of C with A as well as B.

Then, looking at A and B they have the common part shaded which also shows the intersection.

So, the venn diagram represents

C'  ∩ (A ∪ B)

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The measure of the angle R is 116 degrees

To determine the value of the angle, we need to know the properties of a parallelogram.

These properties are;

Then, we have that the angles are;

5x - 14

116

Substitute the angles, we have;

Equate the angles

5x - 14 = 116

collect the like terms, we have;

5x = 116 + 14

add the values

5x = 130

Make 'x the subject

x = 26

Then, <R = 5(26) - 14 = 130 - 14 = 116 degrees

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The balloon's vertical distance above the ground is given as follows:

h = 10.7 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 24º, we have that:

Hence the height is obtained as follows:

tan(24º) = h/24

h = 24 x tangent of 24 degrees

h = 10.7 ft.

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Answer: #3

Step-by-step explanation:

Multiplying eq. 1 by 2 yields [tex]4x+ 2y=-6[/tex]. Adding the 2 equations gives us [tex]7x=-4[/tex], which perfectly eliminates y. Also, looking at the other 3, none of them can successfully eliminate a variable, so 3 is the best choice.

Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

1. Adjusted balance after the first payment: $27,225.

2. Adjusted balance after the second payment: $10,857.

3. Balance at maturity: $10,911.

1. Adjusted balance after the first payment:

Interest accrued in the first 75 days:

= $39,600 x 6% x 75/360

= $495

The adjusted balance after the first payment:

= $39,600 - $11,880 - $495

= $27,225

2. Adjusted balance after the second payment:

Interest accrued in the first 80 days:

= $39,600 x 6% x 80/360

= $528

Adjusted balance after the second payment:

= $27,225 - $15,840 - $528

= $10,857

3. Balance at maturity:

Interest accrued in the remaining 30 days:

= $10,857 x 6% x 30/360

= $54

Balance at maturity:

= $10,857 + $54

= $10,911

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The system of equations -9x+8y = 9x and 7y+8=8x is linear.

A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.

In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).

Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).

Therefore, the system of equations is linear.

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The numerical expression 45 - 6 x 4 can be written in words as "forty-five minus six times four."

In this expression, the order of the operations dictates that we first perform the multiplication of 6 and 4, after that which subtract the end result from the number 45.

Consequently, the expression also can be simplified as follows:

45 - 6 x 4 = 45 - 24

To assess the expression, we subtract 24 from 45:

45 - 24 = 21

Therefore, the final result of the numerical expression 45 - 6 x 4, written in words, is "twenty-one."

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The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

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Answer:

i find my answer as 0

Step-by-step explanation:

perimeter=2(l+w)

2(3x+6+x+2)

x=-2

then substitute for x in the figure above then you'll find perimeter as 0

The equation of the regression line is given by -

y = 20.4x + 1118

Linear regression is used to model the relationship between two variables and estimate the value of a response by using a line-of-best-fit. Refer to the line of best fit plotted for the data given. We can calculate the slope and y - intercept of the line of best fit as -

Slope{m} : 20.40

y - intercept {c} : 1118

So, the equation of the regression line is given by -

y = 20.4x + 1118

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The probability of event B is P(B) = 1/2

From the Venn diagram, we can observe that there are two events A and event B

n(A ∪ B) = 6 + 6 + 20

n(A ∪ B) = 32

And n(A ∩ B) = 6

The sample space would be,

n(S) = 6 + 6 + 20 + 20

n(S) = 12 + 40

n(S) = 52

And the number of outcomes for event B would be,

n(B) = 20 + 6

n(B) = 26

Using the definition of probability,

P(B) = n(B)/n(S)

P(B) = 26/52

P(B) = 1/2

This is the required probability.

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Answer:

0.50

Step-by-step explanation:

The difference between the exact value and the approximate value is -15 L.

In this case, the exact value is 120 L, which means that this is the true and precise value of the quantity being measured. The approximate value is 135 L, which is close to the true value but may have been rounded or estimated.

The difference between the exact value and the approximate value is given by:

Difference = Exact value - Approximate value

Difference = 120 L - 135 L

Difference = -15 L

Therefore, the difference between the exact value and the approximate value is -15 L.

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Answer:

-15

Step-by-step explanation:

-3 multiplied by 5 is equal to -15. When multiplying two numbers with different signs, the product will always be negative. In this case, -3 is a negative number and 5 is a positive number. Thus, their product will be negative. To calculate the product, we simply need to multiply the absolute values of the two numbers and then add the negative sign as the result. The absolute value of -3 is 3, and the absolute value of 5 is 5, so 3 multiplied by 5 is 15. Adding the negative sign gives us the answer of -15.

 Answer:  -15

Step-by-step explanation:

multiply 5 times -3 which equals 15

The equation of the ellipse is equal to x² / 9 + y² / 36 = 1.

In this problem we must determine the equation of an ellipse with vertices at point (0, - 6) and (0, 6) and with an eccentricity of 5 / 6. This can be done by means of the following expression:

(x - h)² / b² + (y - k)² / a² = 1

c = √(a² - b²)

Where:

First, determine the length of the minor semiaxis:

b = √(a² - c²)

b = √(6² - 5²)

b = √(36 - 25)

b = 3

Second, determine the coordinates of the ellipse by midpoint formula:

(h, k) = 0.5 · (0, - 6) + 0.5 · (0, 6)

(h, k) = (0, 0)

Third, write the equation of the ellipse:

x² / 9 + y² / 36 = 1

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Volume is found by multiplying length x width x height

96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Given that, Lena must choose a number between 67 and 113 that is a multiple of 4,6, and 8.

Start listing the multiples of 4 between 67 and 113, which are 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, and 108.

We can then narrow down the list by looking for the multiples of 6, which are 72, 78, 84, 90, 96, and 102, and the multiples of 8, which are 72, 80, 88, 96, 104, and 112.

Since 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

Therefore, 96 is the smallest number that is a multiple of 4, 6, and 8 and is between 67 and 113.

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Lyle will use 8 cups of shredded cheese to make five pizzas.It's important to note that the answer may vary depending on the size of the pizzas and how much cheese Lyle wants to use on each pizza. However, based on the given information, we can conclude that Lyle will need 8 cups of shredded cheese to make five pizzas.

To solve this problem, we need to first find out how much cheese Lyle uses to make one pizza, and then multiply that by the number of pizzas he wants to make.

Lyle uses 1 3/5 cups of shredded cheese to make one large pizza. To find out how much cheese he uses to make one pizza, we can add the      whole number (1) to the fraction (3/5) to get a mixed number:

1 3/5 = 8/5 cups.

Lyle uses 8/5 cups of shredded cheese to make one pizza.

To find out how much cheese Lyle will use to make five pizzas, we can multiply the amount of cheese he uses for one pizza (8/5 cups) by the number of pizzas he wants to make (5):

8/5 cups x 5 pizzas = 40/5 cups = 8 cups.

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