The score on his next test must be at least 97 to get an average score of at least 85.
What is Average Value?Average value of a set of numbers is a single number which represents the whole numbers in the set.
Average value of a set of numbers is calculated by dividing the sum of all the numbers by the number of values in the set.
Here is is given that,
Jerrod had scores of 75, 82, 94 and 77 on his first four history tests.
We need to find the score of his next test such that the average of all is at least 85.
Let x be the score of his next test.
(75 + 82 + 94 + 77 + x) / 5 ≥ 85
75 + 82 + 94 + 77 + x ≥ 85 × 5
328 + x ≥ 425
x ≥ 97
Hence Jerrod must have at least a score of 97.
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If the measure of angle ø is 3pie/4, which statements are true?
The measure of the reference angle is 45°.
cos (0) = √2
sin (0) = √2
The measure of the reference angle is 60°.
The measure of the reference angle is 30°.
tan (0) = 1
Find 3π/4 in degrees
(3(180))/43(45)135°Referance angle
π-3π/4180-13545° or π/4Option A
TanØ=sinØ/cosØ=√2/√2=1Answer:
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]
A number $x$ is equal to $7\cdot24\cdot48$. What is the smallest positive integer $y$ such that the product $xy$ is a perfect cube?
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:
Let theta be an angle in quadrant iv such as sin theta = -5/8. find the exact value of sec theta and cot theta
Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:
[tex]\sec{\theta} = \frac{8\sqrt{39}}{39}[/tex][tex]\cot{\theta} = -\frac{\sqrt{39}}{5}[/tex]Which trigonometric identity relates the sine and the cosine of an angle?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].
What is the secant of an angle?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]
What is the cotangent of an angle?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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Based on an 8-hour day, the number of hours worked in a hospital food service department was 55,267/yr., and the total number of hours paid was 59,995/yr. The actual number of productive FTEs was:
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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Two boys, John and Peter, are running a 100-meter race. In the first race that they run John beats Peter by 5 meters. To make things fair, the next time they race John stands 5 meters behind the starting line. If they run at the same speed as the first race, who will win the second race
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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Multiple choice ( easy)
What is the length of Xpy in terms of
10 m
Options
900л m
15л m
5л m
307 m
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
Which expression can be used to find 52% of 230?
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 =
Jenny made $120 for 8 hours of work. How much would jenny make for 40 hours of work? Use a proportion to show your work in the space provided.
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
6.6x 10⁵ in standard notation
Answer:
660000
Step-by-step explanation:
Store A has sold 67 mugs and sells 11
mugs every week. Store B has sold 13
mugs and sells 17 mugs every week.
How many weeks (w) will it be before
Store B sells as many mugs (m) as
Store A?
m = 11w + 67
m = 17w + 13
[?] weeks
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.
Find the midpoint between
-7 + 4i
and
3 - 2i
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.
Tiffany started a doggle daycare where she offered a variety of services, including grooming. She charges an hourly rate of
$9 and a fee for each service.
Fluffy's human paid $58 for her 3 hour stay. Complete the function for a visit of x hours which includes grooming.
Express the function in slope-intercept form.
The linear function in slope-intercept form for the cost of a visit of x hours is given as follows:
C(x) = 9x + 31.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.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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7. Find the equation of the line passing through the
points P(-2,7) Q(2,-3)
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]
Point W is located at (-5, -3).
Select all of the following that are 5 units from point W.
Choose all answers that apply:
A. (-5, 2)
B. (−8,−5)
C. (-5, 0)
The point that is 5 units from W is (A) (-5, 2)
How to determine the points?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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The prism shown in the diagram has a volume of 39 units^3. What is the volume of the pyramid? Explain your reasoning. I WILL GIVE BRAINLIEST ASAP FOR A QUICK ANSWER
The volume of the pyramid is 13 units³.
What is the volume of the pyramid?
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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The Hartman family is saving $400 monthly for Ronald’s college education. The family anticipates they will need to contribute $20,000 toward his first year of college, which is in 4 years. Which best explains whether the family will have enough money in 4 years?
The family will not have enough money. They will have saved only $16,000.
The family will not have enough money. They will have saved only $19,200.
The family will likely have enough money. They will have saved $16,000 and have accumulated interest.
The family will likely have enough money. They will have saved $19,200 and have accumulated interest.
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.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount 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.
SavingsAmount Hartman family saves monthly = $400Amount needed = $20,000Number of years = 4Number of months = 4 × 12 = 48Amount saved in 4 years = Amount Hartman family saves monthly × Number of months
= $400 × 48
= $19,200
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The following triangle is an isosceles triangle. What is the length of the missing side?
Considering that we have an isosceles triangle, the length of the missing side is of 11 inches.
What is an isosceles triangle?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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Find the nth term of the arithmetic sequence (an) whose initial term a and common difference d are given below. What is the forty-fifth term?
a₁ = 2; d = 1/4
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)
SetupYou 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)
SolutionEvaluating 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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Need help with number 3 inequalities with variables on both sides
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!
Find the equation of a straight line passing through the points (2, -2) and (3, -4)
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
Consider the expansion of (x^2+px-3)(3x-5),where p is a constant.If the coefficient of x of the expansion is -44,find the value of p
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
The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.
A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68.
Which statement describes the amounts the team charged for wrapping gifts?
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
Daphne is calculating the total asset turnover ratio of a company. Under which accounting principle would she value the assets of the company at their original cost? A. accrual method of accounting B. historical cost accounting C. business entity concept D. going concern concept
The accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.
What 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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Johnny created a chart using stick people to depict the frequency of the data. What type of chart did Johnny create
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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Alex scored 40 marks out of 60 in a spelling test pet scored 65% in the same test who did better
Based on the test by result, Alex did better in the test by scoring 66.67%
PercentageAlex = 40 out of 60Percentage scored by Alex = 40/60 × 100
= 0.66666666666666 × 100
= 66.6666666666666
= 66.67%
my Percentage scored by pet = 65%Therefore, Alex did better in the test
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Riley bought a 7 1/2 pounds of clay for the students in her pottery class. She then divided the clay into 4 equal pieces for her students to use for making vases and pots. How much did each piece weigh?
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
Do the points (1,2) , (51,27) and (91,48) lie on a straight line? give reason for your answer
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.
A company has made a rubber ball for $0.02 per square foot. the company wants to spend a maximum of $1 each on a new ball. what is the diameter of the new ball to the nearest tenth of a foot?
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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please help me to get an answer thanks
Answer:
A=P(1+in)
A=13000(1+6/100×9)
A=press calculator
You’re taking a 33 question multiple choice test. Each question has 4 choices. Clueless on 1 question, you decide to guess. What’s the chance you’ll get it right?