A rectangle has a length that is 7 feet longer than its width. Its perimeter is 26 feet. What is the width of this rectangle?

Answer:

x ≈ 17

Step-by-step explanation:

using the cosine ratio in the right triangle

cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] ( multiply both sides by x )

x × cos62° = 8 ( divide both sides by cos62° )

x = [tex]\frac{8}{cos62}[/tex] ≈ 17 ( to the nearest whole number )

The probability that there will be at least 81 cartoons on a coming Saturday is given as follows:

0.011 = 1.1%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 65, \sigma = 7[/tex]

The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:

Z = (81 - 65)/7

Z = 2.29

Z = 2.29 has a p-value of 0.989.

Hence:

1 - 0.989 = 0.011 = 1.1%.

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The length of JG is 5 units if ∠EDH ≅ ∠EDG. Thus option b is the correct answer as per the given relation.

The Given data is as follows:

∠EDH ≅ ∠EDG

Here in the question it is given that, ∠EDH is similar to ∠EDG

The corresponding sides of two triangles are congruent are similar to each other.

EH=9, EJ=4.

EH = EG

EG = 9 -------equation(1)

EG = EJ+JG

EG = 4+JG -------equation(2)

From equations 1 and 2, we get

9 = 4 + JG

9 - 4 = JG

JG = 5 units

Therefore, we can conclude that the length of JG is 5 units.

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The complete question is-

In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?

a. 4 units

b. 5 units

c. 6 units

d. 9 units

Answer: 5

Step-by-step explanation:

∠EDH ≅ ∠EDG, EH=9, EJ=4.Corresponding sides of two triangles are congruent.                         (CPCTC)              .... (1)From the given figure it is clear that        ... (2)Using (1) and (2), we getSubtract 4 from both the sides.

The correlation coefficient between X and Y is approximately -0.483.

We must first determine the mean and standard deviation for both X and Y in order to calculate the correlation coefficient between X and Y.

X has a mean of:

(-5 + 1 + 2 + 11)/4 = 2.25 is the mean of X.

Y has a mean of:

average of Y = (5 + 3 - 3 + 0)/4 = 1.

The value of X's standard deviation is

s_X = sqrt([(-5 - 2.25)^2 + (1 - 2.25)^2 + (2 - 2.25)^2 + (11 - 2.25)^2]/3) = 5.1478

The value of Y's standard deviation is

s_Y = sqrt([(5 - 1)^2 + (3 - 1)^2 + (-3 - 1)^2 + (0 - 1)^2]/3) = 3.7712

After that, we can figure out the correlation between X and Y:

cov(X, Y) = [(-5 - 2.25) × (5 - 1) + (1 - 2.25) × (3 - 1) + (2 - 2.25) × (-3 - 1) + (11 - 2.25) × (0 - 1)]/3 = -7.25

We can finally determine the correlation coefficient:

r = cov(X, Y)/(s X, s Y)=-7.25/(5.1478 3.7712)=-0.483

Thus, roughly -0.483 is the correlation coefficient between X and Y.

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Answer: The total number of possible outcomes in the lottery can be calculated by finding the number of ways to choose 5 distinct numbers out of 70, and then multiply that by the number of possible choices for the gold ball (1 out of 25). So:

Total number of outcomes = (70 choose 5) * 25 = 25,989,600

To win the jackpot, the player must match all 5 white ball numbers and the gold ball number. The number of ways to do this is simply 1, since there is only one winning combination.

Therefore, the probability of winning the jackpot with a single ticket is:

Probability of winning = (number of winning outcomes) / (total number of outcomes) = 1 / 25,989,600

So the probability of winning the jackpot with a single ticket is approximately 0.00000003846, or 1 in 25,989,600.

Step-by-step explanation:

The radius is equal to the length of the given line segment GH, which is 20 units. In this case, r = 20, and θ = 90° = π/2 radians.

Arc GJ is the portion of the circumference of circle H that lies between points G and J. Arc GJ can be calculated using the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = GH = 20 and θ = 90° = π/2 radians. Therefore, l = 20π/2 = 10π. Therefore, the length of arc GJ is 10π units.For example, if the radius of circle H is 10 units, l = 10π/2 = 5π. Thus, the length of arc GJ would be 5π units.To calculate arc GJ, we must first determine the radius of circle H. The radius is equal to the length of the given line segment GH, which is 20 units. We then use the formula l = rθ, where l is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc in radians. In this case, r = 20, and θ = 90° = π/2 radians.

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Answer:

Since the interest is not compounded, Brian will earn a simple interest of 5% per year on his initial deposit of $20,000. The formula for calculating simple interest is:

I = P * r * t

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

I = 20,000 * 0.05 * 5 = 5,000

Therefore, Brian will earn $5,000 in interest over the 5-year period. Adding this to his initial deposit of $20,000, we get:

Total amount = $20,000 + $5,000 = $25,000

Therefore, Brian will have a total of $25,000 in his savings account after 5 years.

Answer:

$25,000

Step-by-step explanation:

The total amount Brian will have in 5 years can also be calculated using the formula for simple interest:

A = P(1 + rt)

where:

A = the total amount

P = the principal (initial balance)

r = the annual interest rate

t = the time period (in years)

In this case:

P = $20,000

r = 0.05 (since 5% is the annual interest rate)

t = 5 (since we're calculating the total amount after 5 years)

Plugging these values into the formula, we get:

A = $20,000(1 + 0.05 x 5)

A = $20,000(1.25)

A = $25,000

So we get answer of $25,000, which is the total amount Brian will have in 5 years.

The yearly percent change in the number of animal species is approximately -67.68%. This means that the number of animal species is decreasing by about 67.68% each year after the last ice age began.

The yearly percent change of the number of animal species after the last ice age began can be calculated by taking the derivative of the function given, S(t)=4,200,000⋅(0.72)t. Using the power rule, the derivative of this function is S'(t)=2,976,000⋅(0.72)t-1. This tells us that the yearly percent change in the number of animal species is -72%. This means that every year, the total number of animal species decreases by 72%.

The yearly percent change of the number of animal species can be determined by finding the derivative of the function [tex]S(t) = 4,200,000(0.72)^t.[/tex]

The derivative of the function can be calculated as follows:[tex]S'(t) = 4,200,000 ln(0.72) (0.72)^t[/tex] The yearly percent change can be calculated by finding the percentage change in the total number of animal species for each year. This can be done by finding the percentage change in the value of the function for each year.

The percentage change in the value of the function can be calculated using the formula:% change = [(new value - old value) / old value] x 100Substituting the values of the function for different years in the above formula, we can find the percentage change for each year.

For example, if we want to find the percentage change in the number of animal species after 10 years, we can substitute t = 10 in the function and calculate the new value of S(t). Then, we can use the above formula to find the percentage change in the value of the function for 10 years.S(10) = 4,200,000(0.72)^10 ≈ 1,357,747% change = [(1,357,747 - 4,200,000) / 4,200,000] x 100 ≈ -67.68%

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 11 &\implies x -11=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -11 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{3em}1( x +2 )( x -11 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-9x-22=f(x) \end{array}} ~\hfill[/tex]

The equation for the line with a slope of 5/6 and passing through the point (22,12) is y=5/6x - 16.

The equation for the line with a slope of 5/6 and passing through the point (22,12) can be expressed as y=5/6x + b. To calculate the value of b, we can plug in the given point's coordinates, (22,12), into the equation. This will result in the equation 12=5/6(22)+b. Solving for b, we get b=-16. Therefore, the equation for the line is y=5/6x-16.

In summary, we can express the equation for the line with a slope of 5/6 and passing through the point (22,12) as y=5/6x - 16. To calculate the value of b, we plugged the point's coordinates, (22,12), into the equation, resulting in the equation 12=5/6(22)+b. Solving for b, we got b=-16. Thus, the equation for the line is y=5/6x - 16.

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well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4  and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).

To get the equation of any straight line, we simply need two points off of it, let's use those two above.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}[/tex]

Check the picture below.

Refer to the attached images.

Since the point (2, 3) lies on the line 2x + ky = 19, the value of k is equal to 5.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making k the subject of formula, we have the following:

k = (19 - 2x)/y

Since the point (2, 3) lies on the line, we have:

k = (19 - 2(2))/3

k = (19 - 4)/3

k = 15/3

k = 5.

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Answer:

≈ 18.8 cm

Step-by-step explanation:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.

The area of the square is given as 36 cm^2, so we can find the side length of the square as:

side length = √(area) = √(36 cm^2) = 6 cm

The diameter of the circle is therefore also 6 cm, and the radius of the circle is half the diameter, or 3 cm.

The circumference of a circle is given by the formula:

circumference = 2πr

where r is the radius of the circle.

Substituting in our values, we get:

circumference = 2π(3 cm) = 6π cm

Using a calculator to approximate π to one decimal place, we get:

circumference ≈ 18.8 cm

Therefore, the circumference of the circle inside the square is approximately 18.8 cm.

Answer:

El espacio recorrido en el tercer segundo será de 9 m.

Step-by-step explanation:

Answer:

The length of x is (10√3)/3.

Step-by-step explanation:

Using the trigonometric ratios of a 30-60-90 triangle, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, we have:

x/2 = (5/√3)

Multiplying both sides by 2, we get:

x = 10/√3, which can be simplified to:

x = (10√3)/3

So the length of x is (10√3)/3.

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The 84th percentile of gestations which can be ruled by standard deviation is 282 days.

The lengths of human pregnancies (gestations) can be modeled by a bell-shaped distribution with a mean of 266 days and a standard deviation of 16 days. Use the empirical rule to determine the 84th percentile of the gestations. The empirical rule, also known as the 68-95-99.7 percent rule, is a statistical guideline that states that within one standard deviation of the mean, 68 percent of the data is distributed.

Within two standard deviations of the mean, 95% of the data is distributed. Finally, 99.7 percent of the data is distributed within three standard deviations of the mean. As a result, it's necessary to locate the corresponding z-score for the given percentile to use the empirical rule.

Since we have the mean and standard deviation, we can use the following equation to compute the z-score using the formula: z = (X - µ)/σ where X is the value of interest, µ is the mean, and σ is the standard deviation. From the formula: z = (X - µ)/σX = µ + zσ Substituting the given values in the formula, we get: X = 266 + z(16)We need to find the 84th percentile.

This means that the remaining 16 percent of the data is distributed outside of the mean plus one standard deviation. As a result, the corresponding z-score can be found using a standard normal distribution table or calculator. The standard normal distribution table or calculator gives us the z-score of 1.00 for the 84th percentile. Using this, we can compute the value of X as follows: X = µ + zσX = 266 + (1.00)(16)X = 266 + 16X = 282

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Answer:

To solve the problem, we need to find the maximum height reached by the ball after the 7th bounce, given that each bounce has a rebound height of 20% less than the previous maximum height.

Let's start by finding the maximum height reached by the ball on the first bounce. The ball is dropped from a height of 120.00 inches, so the maximum height reached on the first bounce is:

120.00 inches

For each subsequent bounce, the maximum height reached is 20% less than the previous maximum height. We can express this mathematically as:

maximum height = 0.8 * previous maximum height

Using this formula, we can calculate the maximum height reached on the second bounce as:

maximum height on 2nd bounce = 0.8 * 120.00 inches = 96.00 inches

On the third bounce, the maximum height reached is 20% less than 96.00 inches:

maximum height on 3rd bounce = 0.8 * 96.00 inches = 76.80 inches

We can continue this pattern for each subsequent bounce. The maximum height reached on the fourth bounce is:

maximum height on 4th bounce = 0.8 * 76.80 inches = 61.44 inches

The maximum height reached on the fifth bounce is:

maximum height on 5th bounce = 0.8 * 61.44 inches = 49.15 inches

The maximum height reached on the sixth bounce is:

maximum height on 6th bounce = 0.8 * 49.15 inches = 39.32 inches

Finally, the maximum height reached on the seventh bounce is:

maximum height on 7th bounce = 0.8 * 39.32 inches = 31.46 inches

Therefore, the maximum height reached by the ball after the 7th bounce is approximately 31.46 inches. Rounded to the nearest hundredth, this is 31.45 inches.

From the given expression, 3/4(8x+12)+x-5, the simplified expression is 7x + 4.

From the question, we are to simplify the given expression.

To simplify the expression 3/4(8x+12)+x-5, we can follow the order of operations, which is commonly remembered using the acronym PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Using PEMDAS, we can simplify the expression as

3/4(8x+12)+x-5

Distributing 3/4 to the terms inside the parentheses

= 3/4 * 8x + 3/4 * 12 + x - 5

Simplifying the multiplication

= 6x + 9 + x - 5

Combining like terms

= 7x + 4

Hence, the simplified expression is 7x + 4.

Here is the complete question:

Simplify 3/4(8x+12)+x-5

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As X is a discrete uniformly distributed random variable with a mean of 5, a variance of 4, and a range of values from 1, 2, 3, 5, 6, 7, 8, and 10, we know that X can have any one of these values with an equal probability of 1/10.

Calculating the likelihood that X will have a number equal to or greater to 6 is necessary to get [tex]P(X > =6)[/tex]. Due to the fact that X is a continuous uniformly distributed random variable.

We may calculate this probability simply counting all number of potential values for X that are greater or equal to to 6, dividing by the entirety of the potential values for X, and then adding the results together.

The probability of X is more than or equivalent to 6 is given by the fact there are a total of 5 variables of X that are at least equal to 6, namely: 6, 7, 8, 9, and 10.

[tex]P(X > =6) = 5/10 = 1/2[/tex]

Thus, (b) 1/2 is the right response.

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The sοlutiοn οf the given prοblem οf cubοid cοmes οut tο be the cubοid has a density οf abοut 6.0 g/cm³.

In geοmetry, a hypercube is a cοncrete οr muti shape. A hypercube is a cοnvex pοlygοns with 12 sides, 6 rectangular faces, and 8 edges. A cubοid is anοther term fοr the creature. An οbject with six square sides is called a cube. Bricks and literature are amοng the items fοund in bοxes. The main differences between cubic but alsο cubic are as fοllοws.

Here,

This equatiοn can be changed tο read density = mass/vοlume. Since we already knοw the mass (534 g), we can use the rearranged methοd tο determine the vοlume.

=> Vοlume = L, W, and H, and mass = 534 g.

=>  density equals mass/vοlume

=>  weight = 534/ (L x W x H)

The CRC Encyclοpedia οf Chemistry and Physics states that nickel has a density οf 8.908 g/cm³.

Thus, we can enter this number as a substitute in οur fοrmula tο οbtain:

=>  density =  534/(L, W, H)

=> 8.908 g/cm³.

Tο sοlve fοr density, we can rewrite this equatiοn as fοllοws:

=>  density =  534/(L, W, H)

=>  6.0 g/cm³ (tο 1 decimal place)

Cοnsequently, the cubοid has a density οf abοut 6.0 g/cm³.

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The Quadratic formula in standard form for points (2.5, 1.5), (2,0) and (3,0) are x²-4x + 3.75 = 0 and x² -2x = 0

The standard form of a quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number

The given parameters that will help us to find the equations are

x = 2.5, and x =  1.5

(x-2.5) (x- 1.5)

Opening the brackets we have

x²-1.5x -2.5x + 3.75 = 0

x²-4x + 3.75 = 0

and the second is given as 2,0

x=2 and x=0

(x-2)(x-0)

Opening the brackets we have

x² -0 -2x+0 = 0

x² -2x = 0

Therefore the standard forms for the quadratic equations are x²-4x + 3.75 = 0 and x² -2x = 0

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Answer:

length = 3x - 1

Step-by-step explanation:

Area of a rectangle = length x width

or using l = length, w = width and A = area

A = l x w

or

l = A/w

Given
A = 18x² - 6x
w = 6x

l = 18x²- 6x/6x

= 18x²/6x - 6x/6x

= 3x - 1

Answer:

3x - 1

Step-by-step explanation:

Area of the Rectangle:

18x^2 - 6x

6x (3x - 1)

Width = 6x

Length =?

Area of Rectangle = Length *  Width

Length = Area/breadth

6x (3x -1) / 6x cross out 6x

Thus, Length of Rectangle = 3x - 1

Answer:

90*

Step-by-step explanation:

Answer: 90 degrees

Step-by-step explanation:

Not sure what its asking but x is at the angle part which is definitely 90 degrees

From the graph and the given information, the value of the given function, fg(-3), is 9

From the question, we are to determine the value of the function, fg(-3).

First , we will determine the value of g(-3)

From the given information,

g(x) = 1/(2 + x)

Substitute x = -3 in the function to determine the value of g(-3)

g(-3) = 1/(2 + (-3))

g(-3) = 1/(2 - 3)

g(-3) = 1/-1

g(-3) = -1

Now,

fg(-3) = f(g(-3))

Thus,

fg(-3) = f(-1)

Now, we will determine the value of f(-1) from the given graph.

From the graph, we can read that the value of f(-1) is 9

Hence,

The value of fg(-3) is 9

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Answer:

2 kph

Step-by-step explanation:

10 kilometers in 5 hours.

1 hour = ?

10/5 = 2 Kilometers

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Answer:

The answer would be the second one.

Step-by-step explanation:

The answer is this because 65% as a decimal is .65 and the second equation is the only one with a .65 in it. It is also the only equation with 24 in it as well.

a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

The definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.

a) The two formulae for cooking times are:

(66 x weight in kg) + (35 x time in an electric oven

Microwave oven time = (26 x weight in kg) + 15

We can compare the two formulae by looking at their coefficients and constants.  This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b) (66 x weight in kg) + (35 x time in an electric oven

2 x 60 = (66 x weight in kg) + 35

120 - 35 = 66 x weight in kg

85 = 66 x weight in kg

weight in kg = 85 / 66

weight in kg ≈ 1.29

So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

Microwave oven time = (26 x weight in kg) + 15

Microwave oven time = (26 x 1.29) + 15

Microwave oven time ≈ 48.34 minutes

Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

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Answer:

34 m x 18 m

Step-by-step explanation:

No picture shown, but we can do it anyway. If one inch on the drawing is actually 4 meters, multiply each dimension by 4.
The actual length is (8.5 * 4) = 34 meters.
The actual width is (4.5 * 4) = 18 meters.

The actual dimensions of the pool are 34 meters long and 18 meters wide.

Answer:

Step-by-step explanation:

I don't mean to be rude but I think that this question Is wrong because the triangle sides are meant to be equal

Pls I am asking nicely because I want to help

Answer: y=3x-2

Step-by-step explanation

(-8)-(7)/ (-2)- (3) = -15/ -5= 3

y=3x+b

f(-2)= -8

y= 3x+ b

-8= 3(-2)+b

-8=-6+b

add 6 on both sides

b=-2

y=3x-2