The sum of three numbers is 52. The third number is 2 times the first. The second number is 8 less than the first. What are the numbers?

Answer:

1900

Step-by-step explanation:

so lets let x represent the total chips that in the bag.

We know that each chip weight 0.12 grams, and there are 228 grams in total.  ok so, 0.12x=228

Divided 0.12 to each side

0.12x/0.12=228/0.12

x=1900 chips Which  means there are 1900 chips in the bag. I hope this helped you<3 sorry if it didnt:(

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

I can explain how to complete each of the steps you have provided.

1. Draw a point at (1, -2)

This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).

2.

Draw an 8-unit long radius

Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.

3. Using a compass

Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.

4. Using a protractor draw a 70 degree arc

Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.

5. Draw a central angle which intercepts your arc

Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.

6. Draw an inscribed angle which intercepts a 40 degree arc

Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.

7. Draw a tangent line

Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.

8. Draw a secant line

Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.

9. Equation of your circle

The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.

Answer:

5y+4z

Step-by-step explanation:

A coefficent is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression

Answer:

x = -4, 7

Step-by-step explanation:

We are given the graph of the function f(x), and we want to find the values that make the statement f(x) = 0.

f(x) = 0 means that there are certain values that make the value of f(x) (which can be considered as y) equal to 0.

We can look to the graph to help us - we should look at where y is equal to 0, which is the x-axis.

On the x-axis, we can see that the function passes through both -4 and 7 (the graph goes up by 1) on that line.

This means that when either -4 or 7 are substituted into the function (i.e. when they are equal to x), they will make the function equal 0.

So,  it means that x = -4, 7.

On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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Answer:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

Step-by-step explanation:

U.S. drivers spend on average, 51 minutes behind the wheel each day.

This means that at the null hypothesis we test that:

\(H_{0}: \mu = 51\)

Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes?

This means that the alternate hypothesis is:

\(H_{a}: \mu < 51\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

51 is tested at the null hypothesis:

This means that \(\mu = 51\)

The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes.

This means that \(n = 75, X = 46.4, \sigma = 18.8\)

Value of the test-statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{46.4 - 51}{\frac{18.8}{\sqrt{75}}}\)

\(z = -2.12\)

Pvalue of the test:

The pvalue of the test is the probability of finding a sample mean less than 46.4, which is the pvalue of z when X = 46.4.

Looking at the z-table, z = -2.12 has a pvalue of 0.017.

Decision:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

No, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

Given the following data:

A null hypothesis (\(H_0\)) can be defined the opposite of an alternate hypothesis (\(H_a\)) and it asserts that two (2) possibilities are the same.

For the null hypothesis, we would test that:

\(H_o : \mu =51\)

For the alternate hypothesis, we would test that:

\(H_a : \mu < 51\)

The test statistics would be calculated with this formula:

\(Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }\)

Where:

Substituting the given parameters into the formula, we have;

\(Z=\frac{46.4\;-\;51}{\frac{18.8}{\sqrt{75} } }\\\\Z=\frac{-4.6}{\frac{18.8}{8.6603} }\\\\Z=\frac{-4.6}{2.1708 }\)

Z = -2.12.

In Statistics, a p-value also known as the probability value is the probability which occurs when the null hypothesis (\(H_0\)) is true of obtaining a sample mean that is at least as unlikely as what is observed by a researcher or scientist.

From the z-table, a z-score of -2.12 corresponds to or has a p-value of 0.017. Therefore, the p-value for this test is 0.017 > 0.01.

In conclusion, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

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The value of x in the rectangle is 6

The given parameters are

Perimeter = 62

From the figure, we have

Length = 2x

Width = x + 13

The perimeter is calculated as:

P =2 * (L + W)

This gives

2 * (2x + x + 13) = 62

So, we have

2 * (3x + 13) = 62

Divide by 2

3x + 13 = 31

Subtract by 13

3x = 18

Divide by 3

x = 6

Hence, the value of x in the rectangle is 6

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Answer:

The answer is below

Step-by-step explanation:

Let x represent the length of the fence along the stone side and y represent the length of the fence along the wood side. The cost of building the fence C(x) is given by:

C(x) = 100x + 20(2y + x)

C(x) = 100x + 40y + 20x

C(x) = 120x + 40y

Since the area = 7500 ft²,

⇒ xy = 7500

y = 7500/x

\(C(x) = 120x + 40(\frac{7500}{x} )\\\\C(x) = 120x+\frac{300000}{x}\\ \\Differentiating\ with\ respect\ to\ x:\\\\C'(x) =120-\frac{300000}{x^2} \\\\At\ minimum\ cost,C(x)=0\\\\hence:\\\\0=120-\frac{300000}{x^2}\\\\\frac{300000}{x^2}=120\\\\120x^2=300000\\\\x^2=\frac{300000}{120}\\ \\x^2=2500\\\\x=\sqrt{2500} \\\\x=50\ ft\)

\(C"(x)=\frac{600000}{x^3}\\ \\C"(50)=\frac{600000}{50^3}=4.8>0\\\\y=\frac{7500}{x} =\frac{7500}{50} =150\ ft\)

Hence to minimize cost, 50 ft of fence is used along the stone side and 150 ft of fence along the wood side

The solution to the system of equations in this problem is given as follows:

X = [28571

      14286].

The system is defined by the following equation:

X = DX + E.

The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:

Inserting this system into a calculator, the solution is given as follows:

Hence the matrix X is given as follows:

X = [28571

      14286].

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Answer:

The answer for this question is 2 ft

Step-by-step explanation:

12ft÷6ft=2

Answer:

67°

Step-by-step explanation:

In a parallelogram, the opposite angles are always equal to each other.

Answer:

\( y = \sqrt{wz} \)

Step-by-step explanation:

The figure given shows the altitude (y) of a right triangle which is perpendicular to the hypotenuse (CA) of the triangle. The hypotenuse is divided by the altitude into two segments, w and z.

According to right triangle altitude theorem the relationship between y, w, and z is represented as follows:

\( y = \sqrt{wz} \)

This expression represents the value of the altitude, y.

Answer:

y = wz with that check mark thingy over it

Step-by-step explanation:

i got the test

Answer:

13/12

Step-by-step explanation:

hope this helps loves x

Since it says mark all that applies,

The answers are:

\(\frac{13}{12}\) and \(1 \frac{1}{12}\)

Convert \(4\frac{1}{3}\) into a mixed number. That becomes: \(\frac{13}{3}\)

After multiplying the two improper fractions, you get: \(\frac{13}{12}\)

Answer:

KR //MT

Since angle JKR and LMT are equal as they are corresponding angle.

For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.

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Answer:

B

D

D

Step-by-step explanation:

please verify and rate 5 stars and say thank you

y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

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Answer:

Step-by-step explanation:

Answer:

Yes, it is proportional.

You know because if you do $9/3 lbs that = 9/3 = $3 per pound

and

if you do $1.50/0.5 lbs = 1.5/0.5 = $3 per pound

Both of them are $3 per pound, so it is proportional.

Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

It should be noted that the equation to represent the production cost will be y = mx + q.

From the information given, the production cost, represented by y, of a Bluetooth device, is equal to the product of labour cost (m) and number of devices (x) in addition to a constant equipment renting fee (q). This will be: y = mx + q.

Changing the subject of the formula to m will be:

y = mx + q

y - q = mx

m = (y - q)/x

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Answer:

C. populations are non normal and the sample sizes are large.

Step-by-step explanation:

To test hypotheses about the difference between two populations means we deal with the following three cases.

1) both the populations are normal with known standard deviations.

2)both the populations are normal with unknown standard deviations.

3) both the populations are non normal in which case both the  sample sizes are necessarily large.

So option C is the correct answer.

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

$340

Step-by-step explanation:

From the information given we know that $204 is the price after a 40% discount is applied which means that this value represents 60% of the regular price and you can find the answer using the rule of three:

204 →  60%

 x    ← 100%

x=(204*100)/60=340

According to this, the answer is that the regular price of the product is $340.

340*0.4= 136

340-136=204

Explanation:

Concept:

The product of two matrices is undefined whenever the rows of the first matrix (reading right to left) do not match the column of the second matrix. However, say that I would need (for some reason) to multiply a 3x3 matrix by a 2x3 one.

Hence,

The final answer is OPTION C