Ruth has 12 feet of ribbon.
She uses 7 feet of it for a craft project and gives 28 inches of it to her sister.
How many inches of ribbon does she have left?
Enter your answer in the box.

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

Answer:

105

Step-by-step explanation:

First, adding two sequence numbers and that result become upper number

Answer:

x=3

Step-by-step explanation:

\(2(5x - 3) = 24\\\\10x-6=24\\\\10x=24+6\\\\10x=30\\\\x=30/10\\\\x=3\)

Answer:

open the bracket by multiplying everything in the bracket by2

then you get

2×5x-2×-3=24

10x-6=24

10x=24+6

10x=30

x=3

The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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Answer:

(A ∪ B) = {15, 17, 19, 20, 21, 23, 25}

Step-by-step explanation:

Multiples of 5:

{0, 5, 10, 15, 20, 25, ...}

So between 14 and 26:

A = {15, 20, 25}

Odd numbers between 14 and 26:

B = {15, 17, 19, 21, 23, 25}

(A ∪ B)

All numbers that are part of at least one of these sets. So

(A ∪ B) = {15, 17, 19, 20, 21, 23, 25}

The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

A.) The percentage of all possible values of the variable that lie between 5 and 9.

P(5<X<9) = P(X<9) - P(5<X)

               = P(z<1.5) - P(-0.5<z)

               = 0.9332 - 0.3085

               = 0.6247

               = 62.47%

B.) The percentage of all possible values of the variable that exceed 1.

P(X>1) = 1 - P(X<-2.5)

          = 1-0.0062

          = 0.9938

          = 99.38%

C.) The percentage of all possible values of the variable that are less than 4.

P(X<4) = P(X <4)

           = P(z<-1)
           = 0.1587

           = 15.87%

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The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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he two numbers that multiply to -35 and add to get -18 are -5 and 3.

To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.

Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:

-5 + 3 = -2

So, -5 and 3 are the two numbers that multiply to -35 and add to -18.

The value of x for each item is given as follows:

a) x = 3.9.

b) x = 32.6º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For item a, we have that x is opposite to the angle of 63º, while 2 is the adjacent side, hence:

tan(63º) = x/2

x = 2 x tangent of 63 degrees

x = 3.9.

For item b, we have that x is the angle, while 7 is the opposite side and 13 is the hypotenuse, hence:

sin(x) = 7/13

x = arcsin(7/13)

x = 32.6º.

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The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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Answer:

$560

Step-by-step explanation:

Answer: The width is 15 yards and the length is 24 yards

Step-by-step explanation:

Let x represent the width of the parking lot in yards

Let the length of the parking lost be (x + 9) as the length is 9 yards greater than the width

So, area = width * length

i.e. 360 = x(x + 9)

360 = x2 + 9x

x2 + 9x - 360 = 0

x2 + 24x - 15x - 360 = 0

x(x + 24) - 15(x + 24) = 0

(x + 24)(x - 15) = 0

Either x = -24 or, x = 15

But as width can not be negative, so we can not have, x = -24

So, we have, x = 15

Therefore, (x + 9) = (15 + 9) = 24

So, we have the following answers.

Width : 15 yards

Length : 24 yards

The equation that models the range of the Indoor Positioning System (IPS) in this hospital is Range^2 = 410,525.

To model the range of the Indoor Positioning System (IPS) in a hospital that measures 860 meters in the east-west direction by 950 meters in the north-west direction, we can consider the range as a function of the distance from the central location. Let's assume the central location is the origin (0,0) on a Cartesian coordinate system.

The range of the IPS can be modeled using the Pythagorean theorem, as it measures the distance between two points in a Cartesian plane. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the range of the IPS can be represented by the equation:

Range^2 = x^2 + y^2

Where x represents the distance in the east-west direction and y represents the distance in the north-west direction from the central location.

Given the dimensions of the hospital (860 meters in the east-west direction and 950 meters in the north-west direction), we can substitute the values into the equation to get:

Range^2 = (860/2)^2 + (950/2)^2

Simplifying this equation, we have:

Range^2 = 430^2 + 475^2

Therefore, the equation that models the range of the IPS for this hospital is:

Range^2 = 184,900 + 225,625

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Answer:

D (Bottom right choice)

Step-by-step explanation:

This is because we have a linear line that changes the same amount every time.

Answer:

The answer is C

Step-by-step explanation:

c.  8√(2^4 )

given 2^(4/8)  can be written as 2^(4×1/8)  

eg: 2^(1/2) is √2 hence same rule we can apply here and since 2^(1/8) we can write as 8√2 and given 2^4

further knowledge: so if asked to expand more we can write it as 8√16 simplifying this further we get 2^(1/2) which is actually √2

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The quadratic function for the value of David's investment indicates;

(i) $45,000

(ii) 9.375 months

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The model of the value of the investment in the bank obtained from the amount of his retirement funds David invested in the bank can be presented as follows;

a = 45 + 75·t - 4·t²

Where;

a = The value of the investment in thousand of dollars after t months

t = The number of months of the investment

(i) The initial amount David invested can be found by plugging in t = 0, in the function for the amount David invested in the bank, as follows;

a = 45 + 75 × 0 - 4 × 0² = 45

The initial amount David invested is; a = $45,000

(ii) The number of months it takes for David investment to reach a maximum value can be found from the quadratic function as follows;

The number of months t(max) at the maximum amount is; t(max) = -75/(2 × (-4)) = 9.375

Therefore, it will take 9.375 months for David's investment to reach a maximum value

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Answer:

see attached

Step-by-step explanation:

We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

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Answer:

The answer is point A' (3, -2).

Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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Answer:

C. .

Irrational numbers are those, which are non-recurring and non-terminating.

I hope it will be useful.

Answer:

C

Step-by-step explanation:

Answer:

To compare the length of the plankton to the length of the jellyfish, we can express the length of the plankton as a percentage of the length of the jellyfish.

First, we need to convert the length of the jellyfish from inches to centimeters so that we can compare the two measurements in the same unit.

12 inches = 12*2.54 = 30.48 cm

Next, we divide the length of the plankton by the length of the jellyfish and multiply by 100 to get the percentage.

0.08 inches / 30.48 cm * 100 = 0.00262 * 100 = 0.262%

So, the length of the plankton is 0.262% of the length of the jellyfish.

Answer:

The plane is:

This is containing the bottom face of the prism

Answer:

cuboid is shown in figure having

the plane is MNOP

Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

The sample variance and standard deviation are given as follows:

Variance = 87.22 %.

Standard deviation = 9.34%.

To obtain the variance and the standard deviation first, we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:

Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10

Mean = 75.85.

Then we must obtain the sum of the differences squared between each observation and the mean, as follows:

(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825

The sample variance is given by the above sum divided by one less than the sample size, hence:

Variance = 784.9825/9

Variance = 87.22 %.

The standard deviation is the square root of the variance, hence:

Standard deviation = sqrt(87.22)

Standard deviation = 9.34%.

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Answer:

Step-by-step explanation:

A and B form a right angle

meaning that A+B=90

if A=58

B=90-58 = 32

answers

B is acute angle, true

second statement is False

Last statement is true