Jerrod had scores of 75, 82, 94 and 77 on his first four history tests. What must he score on the next test to have an average of at least 85? (Note: Remember that average is found by dividing the sum of the numbers, by the number of numbers.)

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]

First, get rid of the denominator by multiplying both sides by 2:

[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]

Add both sides by 6 then subtract both sides by x:

[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]

Then divide both sides by 3:

[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]

Therefore, the answer is x ≤ 2

Answer: [tex]x \leq 2[/tex]

Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get [tex]4x - 6 \leq x[/tex].

Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].

Subtracting x from both sides, we get [tex]3x \leq 6[/tex]

Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]

Hope this helped!

Answer:

y = -2x + 2

Step-by-step explanation:

slope is found with (change in y/change in x), or in this case, (-4--2,3-2), which is -2

with the equation y = -2x + b, solve for b by plugging in the x and y values of one of the points

using (2, -2):

-2 = -2(2) +b

b = 2

so the equation is y = -2x + 2

Answer:

  a₄₅ = 13

Step-by-step explanation:

The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...

  aₙ = a₁ +d(n -1)

You want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...

  a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)

Evaluating this expression, we have ...

  a₄₅ = 2 +44/4 = 2 +11

  a₄₅ = 13

The 45th term of the sequence is 13.

The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

How to find the nth term of the Arithmetic series?

The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.

In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]

We have the find the forty-fifth term of the given series.

= [tex]Tn=a+(n-1)d[/tex]

= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]

= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]

= [tex]Tn = 2+11[/tex]

= [tex]Tn = 13[/tex]

So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

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Answer:

660000

Step-by-step explanation:

Answer:

XPY = 15π m

Step-by-step explanation:

XPY is 3/4 of the circumference of the circle.  The perimeter of a circle is given by 2πr, with r = 10m.

C = 2πr

C = 2π(10)

C = 20π

3/4 of C is (3/4)(20π)

XPY = 15π m

Answer:

Step-by-step explanation:

We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.

Take the first row and set it as an equation:

10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]

Do the same for the second and third rows:

25x + 12y = 86, and

16x +12y =  68

===========

We can take any equation and rearrange it to isolate one of the 2 variables, x or y.  I'll pick 10x = 47-9y and isolate x:

10x = 47-9y

x = (47-9y)/10

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

Now use this definition of x in another equation.  I'll use 25x + 12y = 86.

25x + 12y = 86

25(47-9y)/10 + 12y = 86     [since x = (47-9y)/10 from above]

117.5 - 22.5y + 12y = 86

-10.5y = -31.5

y = 3                                     [the price for decorative wrapping is $3]

If y = 3, then we can use this in any of the equations to find x:

x = (47-9y)/10

x = (47-9(3))/10     [Use y = 3]

x = (47-27)/10

x = 2                              [The price for plain wrapping is $3]

======================

Check to see if these values will expalin the total value of the three rows of numbers:

CHECK:

______UNITS____         $2 each          $3 each

PlainW DecG Total      PlainW ($)      DecG ($)      Total ($)

   x           y                          x                       y

   10         9        $47          $20                    $27              $ 47         OK

   25        12       $86          $50                    $36              $ 86         OK

   16        12       $68          $32                    $36              $ 68         OK

The values work.  Merry Christmas.

Answer:

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Step-by-step explanation:

just did it in edg

Answer:

A=P(1+in)

A=13000(1+6/100×9)

A=press calculator

Answer:

$600

Step-by-step explanation:

For 8 hours she makes $120

For 1 hour she makes $120÷8 = $15

For 40 hours she makes $15 × 40 = $600

Our final answer is $600

Hope this helped and have a good day

Answer:

9 weeks.

Step-by-step explanation:

m = 11w + 67

m = 17w + 13

So:

11w + 67 = 17w + 13

67 - 13 = 17w - 11w

54 = 6w

w = 9.

Considering that we have an isosceles triangle, the length of the missing side is of 11 inches.

An isosceles triangle is a triangle that has two congruent sides.

Researching this problem on the internet, the triangle has two sides of 4 in and 11 in, and one missing side. The missing side is opposite to the side of 4 in, with the same scale, hence the length of the missing side is of 11 inches.

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The linear function in slope-intercept form for the cost of a visit of x hours is given as follows:

C(x) = 9x + 31.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the rate means that the slope is of m = 9. When x = 3, C(x) = 58, hence the y-intercept is found as follows:

C(x) = 9x + b

58 = 9(3) + b

b = 31.

Hence the equation is:
C(x) = 9x + 31.

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The diameter of a new ball is 4.0ft

According to the statement

we have given that the the company wants to spend a maximum of $1 each.

And we have to find a diameter of a new ball.

Remember that for a sphere of diameter D, the surface area is

A = 4*pi*(D/2)^2

In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:

$0.02*A = $1

A = $1/$0.02 = 50

So the surface of the ball must be 50 square feet.

Then we solve:

50ft^2 = 4*3.14*(D/2)^2

D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft

here the diameter of a ball is 4.0ft.

So, The diameter of a new ball is 4.0ft

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Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

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Answer:

No.  They cannon be on the same straight line.

Step-by-step explanation:

As explained in the attached graphic, the slopes are slightly different between the three points.

Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:

The following identity is used, considering an angle [tex]\theta[/tex].

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem we are given the sine, then the cosine can be found as follows:

[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]

[tex]\cos^2{\theta} = \frac{39}{64}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]

In the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].

The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]

The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]

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That year FTE was 26.

According to statement

Labor hours worked that year = 55,267

Total number of hours paid that year = 59,995

The total number of hours during the year

8 hours × 5 days × 52 weeks = 2080 hours

Now we find the FTE per year

So, FTE/YEAR = Labour works on that year / total number of hours in year

Substitute the values in it then

FTE/YEAR = 55267/2080

FTE/YEAR = 26

So, That year FTE was 26.

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Answer:

p = 7

Step-by-step explanation:

(x² + px - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms

= 3x³ +x²(3p - 5) - x(5p + 9) + 15

given the coefficient of the x- term is - 44 , then

-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion

- 5p - 9 = - 44 ( add 9 to both sides )

- 5p = - 35 ( divide both sides by - 5 )

p = 7

Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

According to the statement

We have given that the John and Peter, are running a 100-meter race.

In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.

Here the both participant's speed remain same in both races.

So, We have to find that the If they run at the constant speed as the first race, who will win the second race

So, for this purpose

According to the statement

in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.

So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

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The volume of the pyramid is 13 units³.

A pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces. The volume of a pyramid is one-third that of a prism.

Volume of a pyramid = 1/3 x prism

1/3 x 39 = 13

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Answer: y=[tex]-\frac{5}{2} x+2[/tex]

Step-by-step explanation:

Use the equation of the line format: y = mx + b

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{-3-(7)}{2-(-2)}[/tex]

[tex]m=\frac{-10}{4}[/tex]

simplified

[tex]m=\frac{-5}{2}[/tex]

in order to find B:

[tex]y = -(\frac{5}{2}) *(-2)+b[/tex]

Insert value of y:

[tex]7 = (-\frac{5}{2} ) * (-2) +b[/tex]

Rewrite:

[tex]-\frac{5}{2} * -2 - b=7[/tex]

Cancel the common factor of 2:

[tex]-5 * -1 +b = 7[/tex]

Multiply -5 by -1:

[tex]5 + b= 7[/tex]

Subtract 5 from both sides:

[tex]b = 7-5\\b=2[/tex]

Now substitute values of m, and the final answer is:

[tex]y = -\frac{5}{2}x + 2[/tex]

Hello,

52% of 230 = 52/100 × 230 = 0,52 × 230 = 119,6

Answer:

230 : 100 * 52 =

Step-by-step explanation:

Which expression can be used to find 52% of 230?

The expression is: 230 : 100 * 52 =

The  accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.

Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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Answer:

1.857 pounds

Step-by-step explanation:

If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs

Take the prime factorization of [tex]x[/tex].

[tex]x = 7\times24\times48 = 7\times(2^3\times3)\times(3\times2^4) = 2^7\times3^2\times7[/tex]

If [tex]xy[/tex] is a perfect cube, then the smallest [tex]y[/tex] that makes this happen is [tex]y=2^2\times3\times7^2 = \boxed{588}[/tex]. We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.

Answer: 588

Step-by-step explanation:

Johnny created a Tally marks chart.

A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.

Tally Marks are used to keep a track of numbers in the quickest possible way. Tally marks are used for counting and are represented as a set of five lines in which there are four vertical lines (one vertical line is made for each of the first four numbers) and the fifth number is represented by a diagonal line across the previous four numbers. It can be understood through the given figure

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Answer:

-2+i

Step-by-step explanation:

-7+4i represents (-7,4) and 3-2i represents (3,-2).

So, the midpoint is (-2,1), which represents -2+i.

The point that is 5 units from W is (A) (-5, 2)

The point is given as:

W= (-5, -3)

A point 5 unit from W can be any of the following

W' = (-5 ± 5, -3)

W' = (-5, -3 ± 5)

When the above expressions are evaluated, we have:

W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)

Hence, the point that is 5 units from W is (A) (-5, 2)

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Find 3π/4 in degrees

Referance angle

Option A

Answer:

The measure of the reference angle is 45°.

[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

Reference Angle:  The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).

To convert radians to degrees, multiply by 180/π:

[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]

Positive angles are drawn in a counterclockwise direction from the x-axis.

(See attached for diagram of the angle θ and its reference angle).

Angles on a straight line sum to 180°.

Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:

[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]

The angle 135° lies between 90° and 180° and so is in Quadrant II.

Therefore, the exact trigonometric ratios for 135° are:

[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]

[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]

[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]

Therefore, the true statements are:

  The measure of the reference angle is 45°.

  [tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]