Find the length of the third side, if necessary write in simplest radical form

The z-score for the value 93, when the mean is 100 and the standard deviation is 3 is solved to be

Z scores is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of the parameters

mean, μ  = 100

standard deviation, σ = 3

sample score, X = 93

z score for the score of 93

z = (X - μ) / σ

substituting into the formula

z = (93 - 100) / 3

= -7 / 3

= -2.333

Hence we can say that the z score is 2.333

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Answer:

x = 13

Step-by-step explanation:

to solve this question you must know that angles in a triangle add up to 180 degrees

therefor 180 = 43 + 62 + (7x-16)

solve for x

180 = 43 + 62 + (7x-16)

180 = 105 + (7x-16)

Now, we can subtract 105 from both sides to get

75 = 7x-16

Next, we can add 16 to both sides to get

91 = 7x

Finally, we can divide both sides by 7 to get

x = 91/7

x = 13

So the value of x that satisfies the equation is 13

Answer:

x = 13

Step-by-step explanation:

Interior angles of a triangle sum to 180°.  Therefore:

[tex]\implies 62^{\circ}+43^{\circ}+(7x-16)^{\circ}=180^{\circ}[/tex]

[tex]\implies 62+43+(7x-16)=180[/tex]

[tex]\implies 105+7x-16=180[/tex]

[tex]\implies 7x+89=180[/tex]

[tex]\implies 7x+89-89=180-89[/tex]

[tex]\implies 7x=91[/tex]

[tex]\implies 7x \div 7=91 \div 7[/tex]

[tex]\implies x=13[/tex]

Answer: [tex]4y=-3x+16[/tex]

Step-by-step explanation:

For there to be infinitely many solutions, the equations must represent the same graph.

The points [tex](0,4)[/tex] and [tex](4,1)[/tex] lie on the line. So, the slope is [tex]\frac{4-1}{0-4}=-\frac{3}{4}[/tex]. As the [tex]y[/tex]-intercept is [tex](0,4)[/tex], the equation is [tex]y=-\frac{3}{4}x+4[/tex].

Multiplying both sides by [tex]4[/tex] yields [tex]4y=-3x+16[/tex].

By applying a linear equation, it is concluded that the slope of the line is 2 and the y-intercept is -4

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is y = mx + k, where m is the slope of the line and k is the y-intercept.

First, we draw a triangle ABC whose vertices are A(0, 8), B(2, 0),C(8, 0)

Then we determine point D as the midpoint of AC, so D(4,4)

Now we use B(2,0) and D(4,4) to determine slope of the line (m):

m = (y₂-y₁) / (x₂-x₁)

    = (4-0) / (4-2)

    = 4/2  

    = 2

To find the y-intercept of the line, we pick one of the points on the line. Let's say we pick point (6,8). Then we put those values into the equation:

y = mx + k

8 = 2*6 + k

8 = 12 + k

k = -4

Thus the y-intercept of the line is - 4

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The solution is, The perimeter is 37inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of one half-circle attached to an equilateral triangle

Therefore,

circumference of the semi-circle = πr

r = 8 / 2 = 4 inches

circumference of the semi-circle = 4π

Hence,

perimeter of the shape = 8+8+8+4π

perimeter of the shape = 24+ 4(3.14)

perimeter of the shape = 24 + 12.56

                                       = 36.56

Therefore, perimeter of the shape = 37 inches (approx)

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It depends on the specific context and the nature of the graph. Without more information about the domain restriction and the graph, it is difficult to say exactly what effect changing the 2 to a 5 would have. However, in general, changing a value in a domain restriction would affect the range of possible input values for the graph and could potentially change the overall shape or behavior of the graph.

The answer is False because It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits

The statement that "an inspector chooses 100 bearings from the container that have mean diameter 2.5009 cm. Because this is outside the specified limits, the container is mistakenly rejected" is not accurate. The mean diameter of 2.5009 cm is calculated from a sample of 100 bearings, and it is only an estimate of the true mean diameter of all the bearings in the container. It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits.

In order to make a decision about whether to reject or accept the container, the inspector should use statistical techniques that take into account the sample size and the level of precision required.

It's also important to note that the tolerance of 0.0006 cm is a very small margin, and it's likely that the manufacturing process can't achieve such a precision. The inspector should consider if the sample size and the precision required are aligned with the manufacturing process.

Therefore, The answer is False because It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits.

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It is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

To determine this:

A 95% confidence interval for a proportion gives us an estimate of the range of values where the true proportion is likely to fall. The interval (0.751, 0.863) means that we are 95% confident that the true proportion of math students who prefer to use a handheld calculator versus computer software for computations falls between 0.751 and 0.863.

Given this information, it is reasonable to believe that more than 75% of math students prefer to use a handheld calculator versus computer software for computations because the lower bound of the confidence interval, 0.751, is above 0.75.

In other words, based on the sample data and the construction of the confidence interval, there is strong evidence that the true proportion of math students who prefer to use a handheld calculator is above 75%.

It's important to note that the confidence interval is only an estimate of the true proportion, and it's possible that the true proportion is not exactly within this interval. However, the 95% confidence level means that if we were to repeat the study many times, in about 95% of the cases, the interval would contain the true proportion.

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30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.

We can find how long was each sprinkler used by substitution method.

Let W = hours of use by the Washington family

65 - W = hours of use by the Bennett family

According to the question we get

15W + 40(65 -W) = 1850

15W + 2600 - 40W = 1850

-25W = -750

W = 30

Now, put the value of W in 65 - W to calculate the hours used by the Bennett family

65 - W = 65 - 30 = 35

Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.

--The given question is incomplete, the complete question is

"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--

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total cost=1.45d

for example

1.45=1.45(1) if d=1

The equation is y = 3x/5 - 1/5.

Based on the position of two lines: m = 3/5

Write the equation of linear function

Substitute: 1 = 3/5 * 2 + b

Rearrange unknown terms to the left side of the equation: -b = 3/5 * 2 -1

Write as a single fraction:

Find common denominator and write the numerators above common denominator: -b = (3*2)/5 - 1

Calculate the sum or difference: -b = (6 - 5 )/5

Divide both sides of the equation by the coefficient of variable: b = -1/5

Substitute: y = 3x/5 - 1/5

Find the required form: y = 3x/5 - 1/5.

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The radius of convergence of series (cn dn)xn is 14.

The radius of convergence of a power series (cn xn) is the distance from the origin to the point beyond which the series no longer converges. It is denoted by R and it's calculated by using the formula:

R = 1/lim sup|cn|^(1/n)

The radius of convergence of a product of two series (cn xn) and (dn xn) is the minimum of the radius of convergence of the individual series.

So, in this case, since the radius of convergence of the series cn xn is 14 and the radius of convergence of the series dn xn is 15, the radius of convergence of the product series (cn dn)xn is

min(14, 15) = 14

Therefore, the radius of convergence of the product series (cn dn)xn is 14.

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Based on the given linear equations, the number of 7th-grade students and 8th-grade students is 120 students and 150 students respectively. Hence, Mia's solution is correct.

The value of h in the given linear equation is determined as follows:

9 rectangles = 270 students

1 rectangle = 30 students

7 + h = 11

h = 11 - 7

h = 4

The number of 7th-grade students and 8th-grade students is then determined as follows:

7th-grade students:

4 * 30 = 120 students

8th-grade students:

5 * 30 = 150 students

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The rate at which the top of the ladder is moving down the wall = 9 feet/second.

This is a problem of right triangle similarity.

We can use the Pythagorean theorem to find the height of the ladder, which is the hypotenuse of a right triangle.

We can use the relationship between similar triangles to find the rate at which the top of the ladder is moving down the wall.

Let x be the distance of the base of the ladder from the wall.

We know that the ladder is 26 feet long, so the height of the ladder is the square root of (26^2 - x^2).

We know that the base of the ladder is moving away from the wall at a rate of 3 feet per second.

So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (height of ladder / x)

When x = 10 feet, the height of the ladder is the square root of (26^2 - 10^2) = the square root of (676) = 26 feet.

So, the rate at which the top of the ladder is moving down the wall is (3 feet/second) * (26 feet / 10 feet) = 9 feet/second.

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The curve's approximate length is 33/16, as mentioned throughout the paragraph.

Curved shapes are those composed entirely of curves. A curved form, such as a circle, an ellipse, a parabola, or an arc, can be two-dimensional. Three-dimensional objects like sphere, cones, and cylinders can also have curved forms. A curved line is one that is not straight. A curve results from a point that is not moving in a straight line.

We'll use the following formula to get the angle of a function:

[tex]\begin{aligned}& L=\int d s \\& d s=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y\end{aligned}[/tex]

Let's now calculate x's derivative:

[tex]\begin{aligned}& \frac{d x}{d y}=\frac{4}{8} y^3-\frac{2}{4} \frac{1}{y^3} \\& =\frac{1}{2}\left(y^3-\frac{1}{y^3}\right)\end{aligned}[/tex]

Okay, now enter this into the ds formula to obtain:

[tex]d s=\sqrt{1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2}[/tex]

Observe that:

[tex]\begin{aligned}& 1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2=1+\frac{1}{4} y^6-\frac{1}{2}+\frac{1}{4 y^6} \\& =\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2\end{aligned}[/tex]

The integral will now be easier to understand:

[tex]\begin{aligned}& L=\int_1^2 \sqrt{\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2} d y=\int_1^2 \frac{1}{2} y^3+\frac{1}{2} y^{-3} d y \\& =\left[\frac{1}{8} y^4-\frac{1}{4} y^{-2}\right]_2^1 \\& =\frac{33}{16}\end{aligned}[/tex]

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The complete question is-

Find the exact length of the curve:

[tex]x=\frac{y^4}{8}+\frac{1}{4 y^2}, 1 \leq y \leq 2[/tex]

The first number will be 8 and the second number will be 7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of the two numbers is 15. The difference between five times the first number and Three times the second number is 19.

Let the first number be 'x' and the second number be 'y'. Then the equations are given as,

x + y = 15                 ...1

5x - 3y = 19             ...2

From equations 1 and 2, then we have

5x - 3(15 - x) = 19

5x - 45 + 3x = 19

8x = 64

x = 8

Then the value of the variable 'y' is given as,

8 + y = 15

y = 15 - 8

y = 7

The first number will be 8 and the second number will be 7.

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Answer:

a = 8

Step-by-step explanation:

The following inequalities will form a rectangle. Hence, the area of a rectangle is [tex]\displaystyle{A=\Delta x \cdot \Delta y}[/tex]

In this case, [tex]\Delta x[/tex] = 5-1 which is 4, and [tex]\Delta y[/tex] = a - 2. Substitute in:

[tex]\displaystyle{24 = 4\cdot (a-2)}[/tex]

Now solve the equation for a-term:

[tex]\displaystyle{24=4a-8}\\\\\displaystyle{24+8=4a}\\\\\displaystyle{32=4a}\\\\\displaystyle{8=a}[/tex]

Therefore, the value of a is 8 to make the region have an area of 24 square units.

If [tex]$f$[/tex]is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of function[tex]$f(x)g(x)$[/tex]as [tex]$x$[/tex] approaches domain[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex]

Let [tex]$M$[/tex]be an upper bound of [tex]$f$[/tex] on the domain . Since [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, there exists a number [tex]$L$[/tex] such that for all [tex]$\epsilon > 0$[/tex] there exists a [tex]$\delta > 0$[/tex] such that for [tex]$x \in A$[/tex] with [tex]$0 < |x - c| < \delta |g(x) - L| < \epsilon[/tex].

Now let [tex]\epsilon > 0Then $|f(x)g(x) - Lf(x)| = |f(x)||g(x) - L| < M\epsilon[/tex]

for all [tex]x \in A$ with $0 < |x - c| < \delta$[/tex]. So [tex]\displaystyle\lim_{x \rightarrow c} f(x)g(x)$ exists and is equal to $Lf(c)[/tex]

If [tex]$f$[/tex] is bounded and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex] exists, then the limit of [tex]f(x)g(x)$[/tex]as [tex]$x$[/tex]approaches[tex]$c$[/tex]also exists and is equal to [tex]$Lf(c)$[/tex].

The complete question is:

Let [tex]$f$[/tex] and [tex]$g$[/tex] be functions defined on a domain[tex]$A$[/tex]. Prove that if [tex]$f$[/tex] is bounded, and [tex]$\displaystyle\lim_{x \rightarrow c} g(x)$[/tex]exists, then [tex]$\displaystyle\lim_{x \rightarrow c} f(x)g(x)$[/tex] exists.

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The variable "difficulty level" in the data set is a categorical variable.

A variable in math is a symbol or letter that is used to represent a number or set of numbers in an equation or expression. Variables can be anything such as x, y, a, b, c, etc. Variables are used to represent unknown values or values that can change. They allow equations and expressions to be flexible and can help make problem-solving easier.

Categorical variables are those that have discrete categories or labels, such as "moderate", "easy", and "hard". They are usually qualitative in nature and do not have numerical values. In this case, the difficulty level of each hole is indicated by a label, which can be used to classify the hole accordingly.

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Answer:

difficulty level

Step-by-step explanation:

took the test

The amount William will have in his account after 4 years is $5737.50.

The formula for compound interest is

A(t) = P(1 + i)^t

where A(t) is the final amount in the account after t years, P is the initial principal or the amount invested, i is the annual interest rate, and t is the number of years.

In this case, P = 5000 dollars, i = 3.5% (expressed as a decimal), and t = 4 years.

So, to find the final amount in the account after 4 years, we can plug these values into the formula:

A(4) = 5000(1 + 0.035)^4

To calculate this we can use a calculator or use the exponential function, in this case, we get:

A(4) = 5000(1.035)^4

= 5000(1.1475)

= 5737.50

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Answer:

Below

Step-by-step explanation:

sin (91) / 30   = sin x / 17

arcsin (17 * sin (91) / 30 ) = x = 34.5  °

sin (119) / 45 = sin (x) / 20

20 sin (119)/45  = sin x

x = arcsin ( 20 sin (119) / 45) = 22.9°

The perimeter of the shaded region is 18 units.

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.

If we connect the centers of the circles, this will form an equilateral triangle.

The two sides of this triangle meeting at any vertex will pass through the points of tangency where one circle meets the other two, these two tangent points form the endpoints of one side of the shaded region.

Since the vertex angle of the triangle = 60°, then the arc formed by one side of the shaded region

= 1/6 the circumference of the circle

= 1/6 × 36

= 6 units

So, the perimeter of the shaded region is 3 times this

= 3 × 6

= 18  units

Therefore, the perimeter of the shaded region is 18 units.

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Given

let the value of geometric mean be a and b

a=12

b=7

we know that,

Geometic mean(G.M)=√ab

=√12×7

=√84

=9.16

the geometric mean of 12 and 7 is 9.16

Answer: 25.0

Step-by-step explanation:

[tex]\frac{x}{\sin 65^{\circ}}=\frac{22}{\sin 53^{\circ}}\\\\x=\frac{22 \sin 65^{\circ}}{\sin 53^{\circ}}\\\\x \approx 25.0[/tex]

The company made 42 candles from 5040 cm³ of wax.

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Given the dimensions of the candle, which is in the shape of rectangular prisms

let l be the length, b be width and h be the height,

length = 5 cm

width = 2 cm

height = 12 cm

total wax needed for 1 candle is calculated by the volume of candle,

V = l x b x h

V = 5 x 2 x 12

V = 120 cm³

number of candles made by 5040 cm³ wax

number of candles = 5040/120

number of candles = 42

Hence, 42 candles are made.

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The complete question is,

A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 2cm wide, and 12cm tall. If the company used 5040cm3 of wax, how many candles did they make?

Answer: $900

Step-by-step explanation:

Jenny earns $375 when she works 5 hours.

So the money she earns per hour of work can be found by dividing 375 by 5, which is 75.

The question is asking for how much money she earns when she works 12 hours. You can find this by multiplying the amount of money earned per hour of work times 12.

75*12 = 900

Therefore, the answer is $900.

Answer:

The measure of 7 is 118 degrees.

Step-by-step explanation:

You use the straight line with the 62 degree angle on it to solve.

The line is equal to 180 degrees so you subtract 62 from 180.

180-62=118

That gives you the answer of 118 degrees :)

there you go

to solve it you flip the equation to 15x+3=y

then add -3 to both sides and you get 15x=y-3 then divide both sides by 15 and you get x=1/15y+-1/15

Cindy gets 117 Canadian dollars as exchange.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that in 2003 the exchange rate between the United States and Canada was three Canadian dollars to two US Dollars

Cindy has 78 US dollars to exchange when she visits Canada

We need to find the number of Canadian dollars could she get in exchange

Let the unknown value be x

Formulate a proportion

3/2=x/78

Apply cross multiplication

3×78=2x

234=2x

Divide both sides by 2

x=117

Hence, Cindy gets 117 Canadian dollars as exchange.

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