Eva has xx dimes and yy quarters. She has at most 18 coins worth a minimum of $3 combined. Solve this system of inequalities graphically and determine one possible solution.

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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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 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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total cost=1.45d

for example

1.45=1.45(1) if d=1

Answer:

5 4/9

Step-by-step explanation:

7/9 of 7

= 7/9 × 7

= 7/9 × 7/1

Multiply top×top and bottom×bottom

= 49/9

means 49÷9

9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So

49÷9 is 5 and 4 leftover.

49 ÷ 9

= 5 4/9

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

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.

Answer:

5x + 190 = 300

[tex]\frac{300-190}{5}[/tex]

Step-by-step explanation:

The equation

5x + 190 = 300 helps us to figure out how many minutes it will take for the tank to be empty.

5x + 190 = 300  Subtract 190 from both sides

5x + 190 - 190 = 300 - 190

5x = 110   Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{110}{5}[/tex]

x = 22

It will take 22 minutes for the tank to be empty.

Answer:

$45 would be the savings of option b

Step-by-step explanation:

A. $70*4=$280

B. $40*4=$160 + $0.25*300=$75

a-b =$45

Please see attached photo for better explanation

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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The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.

What is null hypothesis ?

The null hypothesis is a statement that there is no statistical significance between the results of an experiment and a certain theoretical prediction or postulate. It is usually denoted by H0 and it is a statement of "no effect" or "no difference".

The null hypothesis is that the mean mpg of the vans is equal to the manufacturer's rating of 28.228.2 mpg, and the alternative hypothesis is that the mean mpg of the vans is less than the manufacturer's rating.

We can use the t-test statistic to determine the probability of observing a sample mean as extreme or more extreme than the one computed from the data, assuming that the null hypothesis is true.

The t-test statistic is: (sample mean - population mean) / (standard deviation/sqrt(sample size)) = (28.028.0 - 28.228.2) / (2.62.6 / sqrt(2727)) = -3.34

The p-value is the probability of observing a t-value as extreme or more extreme than -3.34, assuming that the null hypothesis is true. With a sample size of 2727, we can use a t-distribution table to find that the p-value is less than 0.01.

The p-value is <0.01, reject the null hypothesis, vans underperform the manufacturer's mpg rating.

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Scientists use math in experiments when they make measurements, analyze quantitative data, and make predictions based on this data.

This is known because Math is an integral part of Science which is why both subjects ( Science and Math ) are considered STEM subjects.

Scientists use math in an experiment to make measurements, analyze data, and make predictions.

For example, scientists use math to make precise measurements of physical quantities such as length, weight, and temperature. They also use math to perform calculations such as determining the concentration of a substance in a solution or the rate of a chemical reaction.

Scientists also use mathematical models and statistical analysis to analyze data and make predictions about the outcome of an experiment. They use mathematical equations to describe the relationships between different variables and to test hypotheses. They also use statistical techniques to determine the significance of their results and to make inferences about a larger population from a smaller sample of data.

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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?

25x -15y -40z +45 =0 is the equation of the plane that passes through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1).

Let the given points be P(2 , 1 , 2) ,Q(3 , -8 , 6) and R(-2 , -3 ,1)

PQ = (3-2 , -8-1, 6-2)

     =(1 , -9, 4)

PR = (-2 -2,-3-1 ,1-2)

     =( -4 ,-4 ,-1 )

→PQ * →PR = [tex]\left[\begin{array}{ccc}i&j&k\\1&-9&4\\-4&-4&-1\end{array}\right][/tex]

             =(9+16)i + (-16+1)j + (-4 -36)k

              =  25i - 15j - 40k

Therefore , the normal vector to the plane is

→n = (25 , -15 ,-40)

Since , the plane passes through all the three points we can choose any point to find its equation .So,the equation of the plane through the point P(2,1,2) with normal vector

→n = (25,-15,-40) is

25(x-2) - 15(y-1) -40(z-2) =0

⇒25x - 50 -15y + 15-40z+80=0

⇒25x -15y -40z +45 =0

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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.

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 :)

Answer:

Step-by-step explanation:

if 1 = 2 than 3 is 4

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]

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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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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The probability of success is 0.2. The result is obtained by adding the probability of getting 9 and the probability of getting 10.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

The probability of A or B can be calculated by

P(A or B) = P(A + P(B)

A 10-sided die is rolled. Each side of the die is labeled with a number from 1 to 10. A number of 9 or 10 should be rolled to make a player succeed. Find the probability of success!

The number of each side of die are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

The probability of success is the probability of getting 9 or 10.

P(9) = 1/10

P(10) = 1/10

P(9 or 10) = P(9) + P(10)

P(9 or 10) = 1/10 + 1/10

P(9 or 10) = 2/10

P(9 or 10) = 1/5

P(9 or 10) = 0.2

Hence, the probability that a player would succeed is 0.2.

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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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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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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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The area of the triangle APB is 6.75 square inches.

We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.

Draw a perpendicular from P to AB, let the point of intersection be Q.

We know that CQ = DB = 6 inches

That is PC + PQ = 6 inches

PQ = (6 - PC) inches

Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem

PA² = PQ² + AQ²

PA² = (6 - PC)² + (AB/2)²

PA² = (6 - PA)² + (6/2)²

PA² = 36 - 12PA + PA² + 9

12PA = 45

PA = 3.75

So PA = PB = PC = 3.75 inches

Also PQ = 6 - PC = 2.25 inches

The area of a triangle can be found by using the formula:

area = (base * height) / 2.

In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is

= (6*2.25)/2

= 6.75 square inches.

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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]

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]

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

A mathematical method known as mathematical induction is used to demonstrate that a claim, formula, or theorem holds true for every natural number. Step 1 (Base Step) demonstrates the truth of a statement for the starting value.

Here,

Given :  6 ⁿ -1  is divisible by 5

Let,

=> 6 ⁿ -1  

=> 6 ¹ - 1

=>5

P(k) is divisible by 5

P(k+1)=6

k+1−1=6.6k−1

=(5+1).6k−1

=5×6 k+6k−1

=5×6k+5m

=5(6k+m)

P(k+1) is divisible by 5

Therefore , the solution of the given problem of PMI comes out to be

6 ⁿ -1  is always divisible by 5.

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