Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
x = 3 plus-or-minus StartRoot 23 EndRoot
x = 3 plus-or-minus StartRoot 51 EndRoot
x = 3 plus-or-minus StartRoot 41 EndRoot
x = 3 plus-or-minus StartRoot 5 EndRoot

Answer:

The interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

Step-by-step explanation:

For Normal Distribution  N ( μ ; σ ) the Empirical Rule establishes that in the intervals:

( μ  ±  σ )   we find  68,3 % of all values

( μ  ±  2σ ) we find  95,4 % of all values

( μ  ±  3σ ) we find  99,7 % of all values

Then we have a normal distribution  N ( 8,1 ; 2,1 )

3*σ  =  3* 2,1 = 6,3

And   8,1 - 6,3  = 1,8             8,1  + 6,3  = 14,4

Then the interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

Answer:

3\49857

Step-by-step explanation:

Using the z-distribution, it is found that:

a. The hypothesis are as follows:

b. The test statistic is: z = -5.30.

c. The p-value is of 0.

d. The result is significant, hence the null hypothesis is rejected.

e. There is sufficient evidence to support the claim that the percentage has changed.

At the null hypothesis, it is tested if the proportion is still of 72%, hence:

\(H_0: p = 0.72\)

At the alternative hypothesis, it is tested if the proportion is different of 72%, hence:

\(H_1: p \neq 0.72\)

The test statistic is calculated as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which the parameters are:

In the context of this problem, the values of these parameters are:

\(p = 0.72, n = 179, \overline{p} = \frac{97}{179} = 0.5419\)

Hence the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.5419 - 0.72}{\sqrt{\frac{0.72(0.28)}{179}}}\)

z = -5.30.

Using a z-distribution calculator, with z = -5.30 and a two-tailed test, as we are testing if the mean is different of a value, the p-value is of 0.

Since the p-value is less than the significance level of 0.01, it is found that:

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A graph of the image of the figure after a reflection across the x-axis is shown below.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

By applying a reflection over or across the x-axis to triangle GLQ, we have;

(x, y)                →      (x, -y)

G (3, 4)             →      (3, -(4)) = G' (3, -4)

L (1, 2)                →     (1, -(2)) = L' (1, -2).

Q (4, -1)              →      (4, -(-1)) = Q' (4, 1)

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Answer:a

Step-by-step explanation:

The inequality representing the given situation is -

300x + 700y ≤ 7500

Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.

Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.

We can write the inequality as -

300x + 700y ≤ 7500

where -

{x} - number of online ads posted

{y} - number of TV ads poste

Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.

Therefore, the inequality representing the given situation is -

300x + 700y ≤ 7500

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When x = 25 and dx = 7 units per day, the rate of change of time (dt) with respect to x is 1 / (7 units/day).

In the given scenario, we have two functions: R(x) and C(x). Let's use the given information to calculate the rate of change of x with respect to time (dt) when x = 25 and dx = 7 units per day.

To find the rate of change, we can differentiate the functions with respect to x. Let's differentiate both R(x) and C(x) to obtain their derivatives:

dR/dx = 2

dC/dx = 0.02x + 0.3

Now, we need to find dt, the rate of change of time with respect to x. To do this, we can use the chain rule of differentiation, which states that dt/dx = 1 / (dx/dt)

Given that dx = 7 units per day, we can calculate dx/dt:

dx/dt = 7 units/day

Now, we can find dt by taking the reciprocal:

dt/dx = 1 / (7 units/day)

Therefore, the rate of change of time with respect to x is 1 / (7 units/day).

Note that the units cancel out in the reciprocal operation, leaving us with units/day.

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The number that represents the change in altitude a hiker must complete to return to sea level if he is at an altitude of 25 feet below sea level is 25.

When the hiker is at an altitude of 25 feet below sea level, he needs to go up 25 feet to reach sea level. This represents a change in altitude of 25 feet, regardless of the direction it is going.

So the number that represents the change in altitude to return to sea level is 25.

The coordinates of the point Y at the other endpoint is 41

From the question, the given parameters are

Because there is not y coordinates in the coordinates, we can make use of only the x coordinate

So, we have the following equation

Point = Proportion * (Y - X)

Substitute the known values in the above equation

So, we have the following equation

12 = 1/3 * (Y - 5)

Multiply through the equation by 3

So, we have the following equation

36 = Y - 5

Add 5 to both sides of the equation

So, we have the following equation

Y = 41

This means that the conclusion is the coordinate of the point Y is 41

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Answer:

It is 6 since the denominator 3 can be moved to 6 by only multiplying it by 2

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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Answer:

238

Step-by-step explanation:

Your welcome

Answer:

you do area by length times width so it's 3x6 which is 18 when every you do area always multiply lengthxwidth or lxw

Answer:

f(x)= x +3

Step-by-step explanation:

f(x)= x +3, find the relationship between an x and y value.

Answer:

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

Step-by-step explanation:

e2020

The mode of the data represented in this line plot will be 8.

Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.

The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.

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Solution

Given:

Time spent at the park =

Convert this time to minutes

Time spent at the library is 210 minutes fewer than that spent at the park.

This implies the time spent at the library is

The answer is 120 minutes

The point estimate for sales when advertising is $3000 is $5412.

Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.

If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:

Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412

So, the required amount is $5412.

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Answer:

Step-by-step explanation:

Required equations are:

Since d is same for both, we substitute d and solve for x:

They will be at same distance after 3 minutes

Time be x distance be y

Solve for x

Answer:

B. Negative

Step-by-step explanation:

Line is going downwards

Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:

(x + 6) x = 16

Expanding the product and rearranging, we get a quadratic equation:

x² + 6x - 16 = 0

We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:

(x + 8) (x - 2) = 0

This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.

Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.

Therefore, the dimensions of the rectangle are 2 meters by 8 meters.

Step-by-step explanation:

The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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Answer:

Answer:

Below

Step-by-step explanation:

Domain is the set of values x can be for a function .....it looks like this one goes from -2 to 2 with asymptopes at these values:

-2< x < 2  

Range is the 'y' values a graph can have...this one goes from -1.5 -ish to 5.5 ish    

-1.5 <= y <= 5.5

Here is the graph with some lines on it:

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

20 m

Step-by-step explanation:

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

The solution to the system of equations is 3x + y = -19 and -3x + 3y = 3 is (-5, -4)

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

3x + y = -19

-3x + 3y = 3

Next, we plot the graph of the system (see attachment)

Using the graphing function on a calculator, we have the solution to be

(-5, -4)

This is so because the equations 3x + y = -19 and -3x + 3y = 3 intersect at the point (-5, -4) and they are not equivalent equations

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The value of X from the given rectangular figure above would be = 6.5. That is option A.

A rectangle can be defined as a quadrilateral that has four sides, four vertices, and four angles.

In a rectangle, when two diagonal line divides it, the two diagonals are of the same length.

That is;

Line PR = Line SQ

Half of PR = ER

Half of SQ = QE

But QE = 2x

PR = 26

QE = 1/2 × 26 = 2x

13= 2x

X = 13/2

X= 6.5

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Answer:

A. x = 96 and y = 42

Step-by-step explanation:

The required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

Given that,
Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle as shown in the accompanying diagram what are the values of x and y is to be determined.

A triangle with two sides and two congruent angles that are equal each other is called an isosceles triangle.

Here,
For an isosceles triangle,
The measure of the angle opposite to the equal side is equal, So
y = 42°

Now,
The sum of the angles in the triangle° is equal to 180,
x + y + 42 = 180
x + 42 + 42 = 180
x = 96

Thus, the required measure of the angle x and y is given as x =92° and y = 42°. Option A is correct.

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Complete Question:

Leslie placed this ad in Collector Car Monthly.

1957 Chevrolet Nomad station wagon. Tropical

Turquoise, 6 cyl. auto, PS, PW, AM/FM, repainted,

rebuilt transmission, restored two-tone interior.

Mint! Moving, sacrifice, $52,900. 555-4231

(a) If the publication charges $48 for the first three lines and $5 for each extra  line, how much will this ad cost Leslie?  

(b) b. Ruth buys the car for 8% less than the advertised price. How much does she pay?

(c) Ruth must pay her state 6% sales tax on the sale. How much must she pay in sales tax?

Answer:

\(Total = \$53\)

\(Ruth = \$48668\)

\(Sales\ Tax = \$2920.08\)

Step-by-step explanation:

Given

\(Ad = 4\ lines\)

\(Charges: \$48\) --- First 3 lines

\(Additional: \$5\) -- Extra lines

Solving (a) : Determine the total charge

The ad has 4 lines. This means that 3 of the 4 lines will be charged at $48 (in total) while the extra line will be charged at $5 per line

So, the total charge is calculated as:

\(Total = 3\ lines + 1\ line\)

\(Total = \$48 + 1 * \$5\)

\(Total = \$48 + \$5\)

\(Total = \$53\)

Solving (b): How much does Ruth pay?

From the ads, the price of the car is:

\(Price = \$52,900\)

And Ruth pays 8% less.

This means that she pays 92% (i.e. 100% - 8% = 92%)

So, the calculation is:

\(Ruth = 92\% * Price\)

\(Ruth = 92\% * \$52900\)

\(Ruth = \$48668\)

Solving (c): The sales tax

\(Sales\ Tax = Sales\ Tax\% * Amount\ Paid\)

\(Sales\ Tax = 6\% * \$48668\)

\(Sales\ Tax = \$2920.08\)