A right prism with a triangular base has a volume of 195 mm3 . The right prism is 13 mm tall. The triangular base of the prism has a base length of 5 mm .

What is the base height of the triangular base of the right prism? Round your answer to the nearest whole millimeter, if necessary.

The number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

29/sin20° = 32°/sinT

T = (33 × sin20°)/29° {cross multiplication}

m∠T = 23 {to the nearest degree}

m∠S = 180 - (20 + 23)° {sum of interior angles of a triangle}

S = 127°

Therefore, the number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

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Answer: Therefore, the probability of not landing on blue when spinning the spinner once is 62.5%.

Step-by-step explanation:  There are 8 sections on the spinner, and 3 of them are blue. Therefore, the probability of landing on blue is:

P(blue) = 3/8 = 0.375

The probability of not landing on blue is the complement of the probability of landing on blue:

P(not blue) = 1 - P(blue) = 1 - 0.375 = 0.625

To convert this probability to a percentage, we can multiply by 100:

P(not blue) = 0.625 x 100% = 62.5%

The amount of tape that Abigail will use to cover the jewelry box is given as follows:

298 in².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

Hence the amount of tape, given by the surface area, is obtained as follows:

S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)

S = 298 in².

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

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a. The error is that the two factors should be 5s and 3s-7s²+1

b. The student out to multiply the two factors if the product will be 15s²-35s³+5s

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

For example, if we are given an expression , 2x +6. The expression consist of two terms and the common factor between them is 2 . Therefore we bring the 2 out . i.e 2( x+3). This means the two factors are 2 and x+3

Similarly , 15s²-35s³+5s can be factorized by bring out the common factors between the three terms

= 5s( 3s-7s²+1)

This means that the student omitted +1 and she ought to have cross checked by multiplying the two factors back if the product will be the polynomial.

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The measure of angle 3 is 95°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

When we have two parallel lines and they are intersected by a transversal , the angles on the parallel lines are corresponding and equal.

Therefore angle 3 = angle 7

angle 7 = 180-(angle 6) (angles on a straight line)

angle 7 = 180-85

= 95°

angle 3 = angle = 7 = 95°

Therefore the value of angle 3 is 95°

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The area of "shaded-region" formed between the two circles having radius as 14 and 6, is 160π square units.

The area of region between "two-circles" can be calculated as area of the "larger-circle" minus area of "smaller-circle".

The "larger-circle" is having radius of = 14 units;

The "smaller-circle" is having radius = 6 units;

So, we can find the area of the region as:

Area = π(14)² - π(6)²;

Area = π(196 - 36),

Area = π(160),

Therefore, area of the region between the two circles is 160π square units.

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The given question is incomplete, the complete question is

Find the area of the shaded region in the figure below if the radius of the outer circle is 14 and the radius of the inner circle is 6. Keep your answer in terms of π.

When someone aged 20 sets up an IRA retirement account with an APR of 5% and deposits $65 at the end of each month, when he retires at age 65, the account will have a future value of $131,718.42.

b) Compared to the total deposit he made over time ($35,100.00), he generated a total compounded interest of $96,618.42.

The future value can be determined using an online finance calculator, which compounds the interest at 5% over a period of 540 months or 45 years.

Number of years = 45 years (65 - 20)

N (# of periods) = 540 months (45 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $65

Results:

Future Value (FV) = $131,718.42

Sum of all periodic payments = $35,100.00 ($65 x 540 months)

Total Interest = $96,618.42

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After the vertical stretch by factor 3 the function becomes g(x)=3x².

The given function is f(x)=x² is vertically stretched by the factor 3.

When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).

Here, g(x)=3×x²

g(x)=3x²

Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².

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The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

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Answer:

Step-by-step explanation:

The sum of the sequence is 9828

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

First term, a = 12

Common ratio, r = 4

The sum of a finite geometric series is

Sn = a(1 - r^n)/(1 - r)

substitute the known values in the above equation, so, we have the following representation

Sn = 12 * (1 - 4^6)/(1 - 6)

Evaluate

Sn = 9828

Hence, the sum is 9828

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The name of the shape Kimberly forms by connecting the points is a plane shape

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

A shape is formed by connecting points

As a general rule; shapes formed by connecting points are referred to as plane shapes, and examples of them are:

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A relation is called a function when each element in the domain is paired with just one element from the A. Range

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

The incomplete definition of relation

A relation takes the form

Domain : x

Range : y

The values from the domain are then paired with the range

If these values are paired just once, then it is a function

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Here cuz:

Frank got more cuz you see Graham has 1/3  and 3/4 and frank got 3/5 and 1/2 so he got more.

Hope This Helps Cuz!

The graph of f(x) relate to its parent function by B. The parent function has been translated up.

Given that

f(x) = 3x +2 +4

When evaluated, we have

f(x) = 3x + 6

The parent function of the above is

f(x) = 3x

When f(x) = 3x is compared to f(x) = 3x + 6, we have

Difference = 6

This means that the parant function is translated up by 6 units

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The students' line that will be parallel to line d is the line with the same slope as d

The rules are given as

This means that the equations of the function are

Carly: y = x + 2

Ramil: y = 2x + 1

If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d

This is because parallell lines have equal slopes

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Answer:

V = π(5.1^2)(7.1) + (1/3)π(5.1^2)(8.6)

= 184.671π + 74.562π

= 259.233π cubic feet

= about 814.4 cubic feet

The number of bows can Sydney make are 3, we get by division.

Given that Sydney has [tex]1\frac{1}{5}[/tex] yards of ribbon to make bows

Each bow is made from a piece of ribbon that is 2/5 yard long

We have to find the number of bows can Sydney make

To find this we have to divide the total length of ribbon by 2/5

[tex]1\frac{1}{5}[/tex]/(2/5)

6/5×5/2

We get 3

Hence, the number of bows can Sydney make are 3

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Part(A),

The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.

Part(B),

Tennis players should report the median value to show they are less prepared for the tournament.

Part A:

To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:

Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271

Number of data values = 10

Mean = sum of the data/number of data values

Mean = 271 / 10

Mean = 27.1

Therefore, the mean time spent practicing is 27.1 minutes.

To find the median, we need to arrange the data in order from smallest to largest:

12, 12, 20, 22, 26, 29, 31, 31, 40, 68

There are 10 data values, so the median is the average of the two middle values:

Median = (26 + 29) / 2

Median = 27.5

Therefore, the median time spent practicing is 27.5 minutes.

To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:

Mode = 12 and 31

Therefore, the modes for the time spent practicing are 12 and 31 minutes.

To find the range, we need to subtract the smallest data value from the largest data value:

Range = largest data value - smallest data value

Range = 68 - 12

Range = 56

Therefore, the range of time spent practicing is 56 minutes.

Part B:

Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.

The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.

Therefore, tennis players should report the median value to show they are less prepared for the tournament.

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The different committees possible are 10,584. Option A is the answer.

Тhe number оf wаys tо choosе 4 men out оf 9 is givеn by 9C4, which is:

9C4 = (9!)/(4!5!)

= 126

Similаrly, the number оf wаys tо choosе 6 wоmen out оf 9 is givеn by 9С6, which is:

9С6 = (9!)/(6!3!)

= 84

So the tоtal number оf wаys tо choosе a committее consisting оf 4 men and 6 wоmen is:

126 * 84 = 10,584

Тherefore, the аnswer is (А) 10,584.

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The proportion when completed for the triangles is a/c = h/b

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

The right triangles

The first expression in the proportion is a/c

This proportion represents leg/hypotenuse expression

Using this as a guide, we can make use of the following proportion

h/b

So, the complete equation is a/c = h/b

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-3x+y=-1 matches  m=3, (1, 2)

-3x+y=-1 matches  m=3, (1, 2) by point slope form

(5, 2)(6, 5) this matches with y=3x-13 b slope intercept form

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=3, b=2

Slope is 3 and y intercept is 2

This matches with equation y-3x=2

Now m=3, (1, 2)

Let us find equation in point slope form

y-2=3(x-1)

y-2=3x-3

-3x+y=-1

So -3x+y=-1 matches  m=3, (1, 2)

(5, 2)(6, 5) this matches with y=3x-13 by slope intercept form

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Part(2),

The volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3),

The difference in price per cubic inch is $0.0128/in³.

Part(4),

The volume of the cylinder with a radius of 8 inches and a height of 6 inches.

Part(2)

The volume of a cone is given by the formula V = (1/3)πr²h,

where r is the radius and h is the height. The volume of the snowcone is therefore V = (1/3)π(4 cm)²(12 cm) = 201.06 cubic cm.

V = (1/3)π(3 cm)²(12 cm) = 113.1 cubic cm.

Since the volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3)

To compare the cost per cubic inch of the two sizes of cereal boxes, we need to calculate the volume of each box and divide the cost by the volume.

The volume of the family-sized box is V = 3 in x 9 in x 12 in = 324 cubic inches.

The cost per cubic inch is therefore $6/324 in³ = $0.0185/in³.

The volume of the regular-sized box is V = 2 in x 8 in x 9 in = 144 cubic inches. The cost per cubic inch is, therefore, $4.50/144 in³ = $0.0313/in³.

The difference in price per cubic inch is $0.0313/in³ - $0.0185/in³ = $0.0128/in³.

Part(3)

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder with a radius of 6 inches and a height of 8 inches, the volume is V = π(6 in)²(8 in) = 904.78 cubic inches.

For the cylinder with a radius of 8 inches and a height of 6 inches, the volume is V = π(8 in)²(6 in) = 1206.37 cubic inches.

Therefore, the volume of the cylinder with a radius of 8 inches and a height of 6 inches.

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Answer:

C

Step-by-step explanation:

because i did it in school and got it correct sorry if im wrong any way

The product of the matrices is [24].

Given is a row matrix and a column matrix, we need to find the product of both,

So,

A = [-3, 3, 0]

B = [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

Now, the product will be =

AB = [-3, 3, 0] ×  [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]

AB = [9 + 15 + 0]

AB = [24]

Hence the product of the matrices is [24].

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The correlation coefficient for the data shown in the table is: B. -1.

In order to calculate or determine the correlation coefficient for the data shown in the table (see attachment), we would have to determine the slope of the line based on the points as follows;

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (10 - 15)/(5 - 0)

Slope (m) = -5/5

Slope (m) = -1.

Slope (m) = (5 - 10)/(10 - 5)

Slope (m) = -5/5

Slope (m) = -1.

In this context, we can reasonably infer and logically deduce that there is a negative correlation between the data and the correlation coefficient is -1.

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Missing information:

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

Sample Response: Use the inverse operation to isolate the variable. Undo the subtraction of 4 by adding 4 to both sides of the equation. –4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. Check the solution by substituting 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, so 13 is the solution.

Step-by-step explanation:

–4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. check it by taking 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, 13 is the answer

The monomials in the expression are given as follows:

x², xy, -8y².

The simplified polynomial is given as follows:

9x² + 9xy - 72y².

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The expression for this term are given as follows:

9(x² + xy - 8y²).

The inner term is a polynomial composed by the sum/subtraction of the monomials presented as follows:

x², xy, -8y².

Applying the distributive property, the simplified polynomial is given as follows:

9x² + 9xy - 72y².

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Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

We know that,

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:

= (7/8) ÷ (1/6)

To divide fractions, we need to invert the second fraction and multiply:

= (7/8) × (6/1)

Simplifying the fractions, we get:

(7 × 6)/(8 × 1) = 42/8 = 5 1/4

Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.

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