What are the coordinates of point Q.

Answer: He jogs 12 miles per hour

Step-by-step explanation: Every 15 minutes he jogs 3 miles, there are 60 minutes in an hour, 60/15 = 4, 4 x 3 = 12

Answer:

12 nickels, 37 dimes and 22 pennies

Step-by-step explanation:

Let

x ----> the number of nickels

y ----> the number of dimes

z ----> the number of pennies

we know that

1 nickel=$0.05

1 dime=$0.10

1 pennies=$0.01

so

0.05x+0.10y+0.01z=4.52 -----> equation A

y=3x+1 ----> equation B

z=x+10 ----> equation C

substitute equation B and equation C in equation A and solve for x

[tex]0.05x+0.10(3x+1)+0.01(x+10)=4.52 0.05x+0.30x+0.10+0.01x+0.10=4.52\\0.36x+0.20=4.52\\ 0.36x=4.52-0.20\\x=4.32/0.36\\x=12\ nickels[/tex]

Find the value of y

[tex]y=3(12)+1=37\ dimes[/tex]

Find the value of z

[tex]z=12+10=22\ pennies[/tex]

Answer:

2.67 bushels of corn

Step-by-step explanation:

We can see it in the picture.

Answer:

The answer is (C) 8

Step-by-step explanation:

First, let's calculate the length of the side of the square.

[tex]A_{square}=a^2[/tex], where [tex]a[/tex] is the length of the side. Now, let's try to build the square. First we need to find a point which distance from (0, 0) is 10. For this, we can use the distance formula in the plane:

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex] which for [tex]x_1=0[/tex] and [tex]y_1 = 0[/tex] transforms as  [tex]d=\sqrt{(x_2)^2 + (y_2)^2}[/tex]. The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, [tex]x_2[/tex], [tex]y_2[/tex] and 10 are a Pythagorean triple. From this, [tex]x_2= 6[/tex] or  [tex]x_2=8[/tex] while [tex]y_2= 6[/tex] or [tex]y_2=8[/tex]. This leads us with the set of coordinates:

[tex](\pm 6, \pm 8)[/tex] and [tex](\pm 8, \pm 6)[/tex].  (A)

The next step is to find the coordinates of points that lie on lines which are perpendicular to the lines that joins the origin of the coordinate system with the set of points given in (A):

Let's do this for the point (6, 8).

The equation of the line that join the point (6, 8) with the origin (0, 0) has the equation [tex]y = mx +n[/tex], however, we only need to find its slope in order to find a perpendicular line to it. Thus,

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m =  \frac{8-0}{6-0} \\m = 8/6[/tex]

Then, a perpendicular line has an slope [tex]m_{\bot} = -\frac{1}{m} = -\frac{6}{8}[/tex] (perpendicularity condition of two lines). With the equation of the slope of the perpendicular line and the given point (6, 8), together with the equation of the distance we can form a system of equations to find the coordinates of two points that lie on this perpendicular line.

[tex]m_{\bot}=\frac{6}{8} = \frac{8-y}{6-x}\\ 6(6-x)+8(8-y)=0[/tex]  (1)

[tex]d^2 = \sqrt{(y_o-y)^2+(x_o-x)^2} \\(10)^2=\sqrt{(8-y)^2+(6-x)^2}\\100 = \sqrt{(8-y)^2+(6-x)^2}[/tex]   (2)

This system has solutions in the coordinates (-2, 14) and (14, 2). Until here, we have three vertices of the square. Let's now find the fourth one in the same way we found the third one using the point (14,2). A line perpendicular to the line that joins the point (6, 8) and (14, 2) has an slope [tex]m = 8/6[/tex] based on the perpendicularity condition. Thus, we can form the system:

[tex]\frac{8}{6} =\frac{2-y}{14-x} \\8(14-x) - 6(2-y) = 0[/tex]  (1)

[tex]100 = \sqrt{(14-x)^2+(2-y)^2}[/tex]  (2)

with solution the coordinates (8, -6) and (20, 10). If you draw a line joining the coordinates (0, 0), (6, 8), (14, 2) and (8, -6) you will get one of the squares that fulfill the conditions of the problem. By repeating this process with the coordinates in (A), the following squares are found:

Now, notice that the equation of distance between the two points separated a distance of 10 has the trivial solution [tex](\pm10, 0)[/tex] and  [tex](0, \pm10)[/tex]. By combining this points we get the following squares:

See the attached second attached figure. Therefore, 8 squares can be drawn  

Answer:

  y DOES NOT vary directly with x

Step-by-step explanation:

If variation is direct, the ratio of y to x is a constant. Here, we have ...

  11/7 ≠ 13/8

so variation is not direct.

___

It appears that y = 2x-3, rather than y = kx for some k. The added constant (-3) means variation is not direct.

To determine if y varies directly with x, we calculate the ratios between the corresponding values. The ratios are approximately constant, so y varies directly with x. The equation representing the direct variation is y = 1.57x.

To determine whether y varies directly with x, we need to check if the ratio between the corresponding values of y and x is constant. Let's calculate the ratio for each pair of values:

Since the ratios are approximately constant, we can conclude that y varies directly with x. To find the constant of variation (k), we can choose any of the ratios. Let's take the ratio from the first pair: 11/7 ≈ 1.57. Therefore, the equation that represents the direct variation is y = 1.57x.

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Answer:

The answer to your question is:  4 x 10 ⁶ = population of Oregon

Step-by-step explanation:

Data

Population of the USA = 3.2 x 10⁸

Population of the USA = 80 population of Oregon

Process

                           3.2 x 10⁸  = 80 population of Oregon

                           3.2 x 10⁸ / 80 = population of Oregon

                          4 000 000 = population of Oregon

                           4 x 10 ⁶ = population of Oregon

The population of Oregon will be 4 x 10⁶.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The population of the United States = 3.2 x 10⁸

And, The population of the United States is about 80 times the population of Oregon.

Let population of Oregon = x

Then, We can formulate;

3.2 x 10⁸ = 80 × x

Solve for x as;

3.2 x 10⁸ = 80 × x

x = 3.2 x 10⁸ / 80

x = 0.04 x 10⁸

x = 4 x 10⁻² x 10⁸

x = 4 x 10⁶

Thus, The population of Oregon will be 4 x 10⁶.

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Answer:

[tex]8x^8[/tex] (Please see my interpretation of the problem.)

The problem:

Simplify [tex]\sqrt{64x^{16}}[/tex] (Please tell me if I did or didn't interpret your problem correctly. Thank you!)

Step-by-step explanation:

[tex]\sqrt{64x^{16}}[/tex]    (Given)

[tex]\sqrt{64}\sqrt{x^{16}}[/tex] (if u and v are positive then [tex]\sqrt{uv}=\sqrt{u}\sqrt{v}[/tex])

[tex]8\sqrt[2]{x^{16}}[/tex]  ([tex]\sqrt{ }=\sqrt[2]{}[/tex])

[tex]8x^{\frac{16}{2}}[/tex]  ([tex]\sqrt[n]{x^m}=x^\frac{m}{n}[/tex])

[tex]8x^8[/tex]   (simplified/reduced the fractional-exponent)

Answer:

8x8

Step-by-step explanation:

so B

Answer:

The roots are:

a) z1 = 0

b) z2 = -2

c) z3 = ∛2 or 1.26

Step-by-step explanation:

First we factor z from the original equation

       z⁷ + 6z⁴ - 16 z = z ( z⁶ + 6z³ -16)

                                  z ((z³)² + 6z³ -16)             express z⁶ as a power

                                  z (z³ + 8)(z³ -2)                factor

   Now, equal to zero each term

    z1 = 0           first answer

    z³ + 8 = 0         z³ = -8          z2 = -2             second answer

    z³ -2 = 0           z³ = 2            z3 = ∛2 or 1.26   third answer

When determining the roots of a function, you set the function equal to zero and solve for the variable. For example, the roots of the function f(x) = x² - 5x + 6 would be x = 2 and x = 3.

Though the specific function is not provided in the question, the general process to determine all the roots of a function lies in setting the function equal to zero and solving for the unknown variable. The roots of the function are the values of the unknown variable that make the equation true. For example, if you have a function f(x) = x² - 5x + 6, by setting it to zero and following the method you obtain the roots as x = 2 and x = 3.

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Answer:

False.

Step-by-step explanation:

The first two (3:5) & (3 to 5), represents the same ratio.

However, 5/3 does not equal to the others, for it's form would be:

5:3

5 to 3

~

Answer:

false

Step-by-step explanation:

i hope i helped :)

Answer:

Step-by-step explanation:

i can't see graph.

[tex]f(x)=-x^2-2x+15=-(x^2+2x+1-1)+15=-(x-1)^2+1+15=-(x-1)^2+16\\domain=all~real~numbers.\\[/tex]

Range≤16

so A

The domain is all real numbers. The range is y less then or equal to 16.

Quadratic function is a polynomial of degree 2. It is in the form:

f(x) = ax² + bx + c

where a, b, c are constants

The domain of a function is the set of input variables while the range of a function is the set of output variables.

From the image attached, The domain is all real numbers. The range is y less then or equal to 16.

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Answer:  (1) 14.4%   (2) 3.78%   (3) $222.48     (4) 21,176.47    

               (5) $425    (6) 14.3 cents per mile

Step-by-step explanation:

1) This is a calculator question. I = 0.144    --> 14.4%

[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\bullet \text{A = Accrued amount (total amount paid)}\\\bullet \text{P = Principal (initial cost of the car)}\\\bullet \text{r = rate (interest rate in decimal form)}\\\bullet \text{n = number of times in a year (number of months)}\\\bullet \text{t = number of years}\\\\A = m \times nt\\\bullet \text{m = monthly payment amount}\\\bullet \text{nt = number of payments made}\\\implies m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]

2) m = 93.33

   nt = 36

   P = 3000

   n = 12

[tex]m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\93.33\times 36=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\3359.88=3000\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.11996=\bigg(1+\dfrac{r}{12}\bigg)^{36}\\\\\\1.00315198=1+\dfrac{r}{12}\\\\\\0.00315198=\dfrac{r}{12}\\\\\\0.0378=r\\\\\\\large\boxed{3.78\%}=r[/tex]

3) same equation as #2 but deduct the down payment from the Principal

   nt = 42

   P - d = 5,555 - 555 = 5,000

   r = 18% --> 0.18

   n = 12

[tex]m\times nt=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}\\\\\\m\times 42=(5,555-555)\bigg(1+\dfrac{.18}{12}\bigg)^{42}\\\\\\42m=5000(1.015)^{42}\\\\\\42m=5000(1.868847)\\\\\\42m=9344.23557\\\\\\m=\large\boxed{222.48}[/tex]

4)  Gas  +  Oil  = cost per mile × number of miles

   1000 + 800 = 0.085x

               1800 = 0.085x

        [tex]\large\boxed{21,176.47}=x[/tex]

5)  [tex]\text{Annual Depreciation}=\dfrac{\text{Cost of car - Trade-in value}}{\text{Years driven}}[/tex]

[tex].\qquad =\dfrac{3800-1250}{6}\\\\\\.\qquad =\dfrac{2550}{6}\\\\\\.\qquad = \large\boxed{425}[/tex]

6) [tex]\dfrac{\text{(Cost of car - Market value) + Gas & Oil + Parts, Maintenance + Insurance}}{\text{Miles driven}}[/tex]

[tex]=\dfrac{(5000-3800)+750+250+300}{17,500}\\\\\\=\dfrac{2500}{17,500}\\\\\\=0.142857\\\\=\large\boxed{14.3\ cents\ per\ mile}[/tex]

Answer:

9

Step-by-step explanation:

a negative divided by a negative is a positive.

For the first problem, the diver's depth after diving 47 feet and then rising 12 feet is -35 feet or 35 feet below the surface. In the second problem, the temperature rose from -6°F to 7°F by noon.

Let's answer your mathematics problems one by one.

A diver dives 47 ft below the surface of the water and then rises 12 ft. We can use addition by understanding that direction matters. A depth of 47 ft below the surface is represented as -47, while rising 12 ft means +12. So, the final depth could be represented mathematically as -47 + 12, which equals to -35 ft. It means the diver is 35 feet below the surface of the water.

The temperature at 6 AM is -6°F. The temperature rises 13 degrees Fahrenheit by noon. The situation can be mathematically represented as -6 + 13. So, the temperature at noon would be 7°F.

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Answer:

The answer to your question is: the last option 3.0 x 10⁻¹⁰

Step-by-step explanation:

First divide 3.3 by 1.1

                                     3.3 / 1.1 = 3

Then subtract -8 - (2) = -8 -2 = -10

Finally use scientific notation where the power will be -10

            result :                3 x 10 ⁻¹⁰

Answer:

The another term for the 4% value is : Margin of error

Step-by-step explanation:

Dr. Cyril conducts a simple random sample of 500 men.

He finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%.

Now, the another term for the 4% value is : Margin of error

Means the estimate of father being unsure about his ability would be between 19% and 27%.

When sample size is increased, the margin of error becomes smaller.

Answer:

  1

Step-by-step explanation:

Three points define 1 plane.

Answer:

The answer is plane 1

Step-by-step explanation:

Planes X and Y and points J, K, L, M, and N are shown.

Answer:

327692

Step-by-step explanation:

[tex]65536 = (-4)^{8} \\ \\ 65536 \times 5 = 327680 \\ \\ 327680 - 3(-4) = 327680 + 12 = 327692[/tex]

According to the Order of Operations [GEMS(A)\BOMDAS\PEMDAS etc.], in this case, you evaluate the exponent BEFORE multiplying. This is a common mistake people make.

I am joyous to assist you anytime.

Answer:

10 months

Step-by-step explanation:

Let X represent the number of months

The cost equation for the first plan = $20 + 10x

The cost equation for the second plan =$ 40+8x

The number of months at which the cost for the two plans will be equal can be worked out by equating the costs for the two plans and then calculate the value of x.

Thus,

$20+10x = $40 +8x

        10x -8x =$40-$20  

            2x = $ 20

              x= 20/2

                 x= 10

Substituting X in each equation,

  $20 +$10(10) = $40 + $8(10)

   $ 20 +$100 =$40 +$80

       $120 =$120

Thus, the amount after ten months = $120

Answer:

This is random sampling.

Step-by-step explanation:

Given condition is - In a poll, 809 adults were called after their telephone numbers were randomly generated by a​ computer, and 20 % were able to correctly identify the secretary of state.

This research center used random sampling.

Random because the telephone numbers were randomly generated by the computer. It could have been any number and any person.

---------------------------------------------------------------------------------------------

Other sampling methods either use groups to conduct survey or survey the easiest available sample as in convenience sampling. So, rest options are wrong.

Therefore, it is random sampling.

Answer:

  37 1/2 C

Step-by-step explanation:

25 × 1 1/2 C = 37 1/2 C

The temperature would have dropped 37 1/2 C.

_____

The ground temperature is irrelevant to the question.

Answer:

Descriptive statistics

Explanation:

The population average is a descriptive statistic. It informs about how the population looks like, in this case, the population looks like having a average of 1000.

If, using her class's average where to infer the population average that is inferential statistic. But that is not the case

Answer:

Median.

Step-by-step explanation:

We have been given that in​ 2004, the mean net worth of families in a certain region was ​$470.2 thousand and the median net worth was ​$92.3 thousand.

We know that mean and median of a symmetric data set is equal.

We also know that when mean of a data set is greater than median, then the data set has a very large valued outlier.

Since mean net wroth of families is approximately 5 times more than median net wroth of families, this means that some of the families has very high net worth as outliers.

Since the net worth of families has very large outliers, therefore, I would prefer median as the appropriate measure of center as median is not affected by outliers.

Answer:

save 100$ each check.

Step-by-step explanation:

Answer:

I will save $2,600 in one year by depositing $50 dollars per week in a savings account.

Step-by-step explanation:

When you set a goal, it should clearly state what you want to accomplish, it has to be measurable and relevant according to what you want to do. Also, it has to establish a deadline and it should be something that you can achieve.

According to this and the options given, the goal that would be most helpful for Caleb is I will save $2,600 in one year by depositing $50 dollars per week in a savings account because it is well defined, it is measurable and establishes a deadline as he will save $50 dollars per week to get $2600 in a year. Additionally, the goal can be accomplished and it is relevant to what he wants to do that is to save money for living expenses because he is going to college next year.

Answer:

If the length of the garden is (x + 5) then the width will be (x + 3)

The area of the garden is 48 sq feet

Step-by-step explanation:

The garden is x^2 + 8x + 15 sq feet

Use the factorization method and break the middle term:

x^2+3x+5x+15

Group the first two terms and last two terms:

(x^2+3x)+(5x+15)

Take out the common from each pair.

x(x+3) +5(x+3)

(x+5)(x+3)

We have already been given that x+5 is the length. Then this shows that x+5 is the length and x+3 is the width

If the length of the garden is (x + 5) then the width will be (x + 3)

The method I used is the F.O.I.L. method

The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.

(x + 5)(x + 3) = x^2 + 3x + 5x + 15

Solve the like terms:

= x^2 + 8x + 15

b) x= 3 feet

(x + 5)(x + 3)

Substitute the value in the expression

(3 + 3)(5 + 3)= (8)(6)= 48 square feet

Area of the garden is 48 sq feet.

Answer:

There are 49 corrupt senators and 1 honest senator.

Step-by-step explanation:

Freedonia has 50 senators. Each senator is either honest or corrupt. At least one of the Freedonian senators is honest.

As we can see that there are no two senators where both of them are honest. So either there is one senerator who is honest or none.

As given that at least one of the Freedonian senators is honest.

Hence, we can conclude there is one and only one honest senator.

Final answer:

In Freedonia's senate, there must be one honest senator and forty-nine corrupt senators to satisfy the given conditions.

Explanation:

To solve the problem presented, we must work under the conditions that in Freedonia's senate of 50 senators, which implies that there are 50 senators in total, each is either honest or corrupt, at least one senator is honest, and in any pair of senators, at least one is corrupt. This means it's impossible to have two honest senators together, as this would contradict the condition that in any pair of senators, there must be at least one corrupt senator.

Given that there is at least one honest senator, we can use logic to deduce the following: If we were to assume that there are two honest senators, we would have a pair of senators where both are honest, which violates the given condition. Therefore, there can be only one honest senator in Freedonia's senate to meet all the conditions laid out in the problem.

Since the total number of senators is 50, and we have established that there is only one honest senator, it follows that the remaining 49 senators must be corrupt. Hence, the Freedonia's senate consists of one honest senator and forty-nine corrupt senators.

Answer:

  24 209/300 m ≈ 24.69667 m ≈ 24.70 m

Step-by-step explanation:

The total height is the sum of the above-ground height and the below-ground depth:

  6 5/12 m + 18.28 m = (6 + 18) m + (5/12 + 7/25) m

  = 24 m + (125+84)/300 m

  = 24 209/300 m ≈ 24.6966666... m ≈ 24.70 m

_____

The problem statement does not say what rounding is required. The least-resolution number is 18.28, with resolution of 1 cm, so the answer might rightly be rounded to that resolution: 24.70 m. If we take the numbers to be exact, their sum can only be represented exactly as the ratio of integers or a mixed number or a repeating decimal.

The statement 'If x=3, then x−3=0' is justified by the Subtraction Property of Equality. This property allows you to subtract the same value from both sides of an equation while maintaining equality.

The statement 'If x=3, then x−3=0' is justified by the Subtraction Property of Equality. This property states that if you subtract the same number from both sides of an equation, the equation remains equal. So, in this case, you start with x=3 and then you subtract 3 from both sides to get x-3=0. It's also important to note that the other properties mentioned, Division, Reflexive, and Multiplication, aren't appropriate in this scenario because no division, reflexion or multiplication operation is being performed.

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Answer

 B) x + 20 ≥ 50

Step-by-step explanation:

Answer:

B) x + 20 ≥ 50

Step-by-step explanation:

Given,

The hours she already has for social studies = 20,

After getting x more hours,

The total hours she has now = x + 20,

According to the question,

Total hours ≥ 50

[tex]\implies x + 20\geq 50[/tex]

Which is the required inequality to model give situation,

Hence, OPTION B is correct.

Answer: Last option.

Step-by-step explanation:

Observe the figure attached.

In order to find the value of "b", you need to remember the definition of "Alternate interior angles". These are the pairs of angles located in the interior of the parallel lines and on opposite side of the transversal. They are congruent.

Based on this definition, you can conclude that the angle "b" and the angle that measures 128° are Alternate interior angles; therefore they are congruent.

This means that the value of "b" is:

[tex]b=128\°[/tex]

Answer:

The last answer!

Step-by-step explanation:

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