Lindsay's z - score, given the mean score, the standard deviation, and her score, is 2. 35.
How to find the z - score ?To calculate a z-score, you subtract the mean from the individual score and then divide by the standard deviation.
The formula is:
z = (x - μ) / σ
Where
x is the individual score
μ is the mean
σ is the standard deviation.
So, to find Lindsay's z-score:
z = (98 - 78.2) / 8.4
z = 19.8 / 8.4
z = 2.35
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18. A8 x 6 x 4 cm³ metallic cube is melted. Find the minimum volume of molten metal which should be added to
mould it into a cube whose edge is an integer.
(1) 20
(2) 21
(3) 23
(4) 24
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
How to estimate the minimum volume of molten metal?Volume exists as a scalar quantity representing the amount of three-dimensional space encircled by a closed surface.
The minimum volume of a shape with measured dimensions exists provided by the lowest values of the dimensions when accounting for measurement error. Maximum Volume: The maximum volume of a shape with measured dimensions exists provided by the highest values of the measurements when accounting for measurement error.
The volume of the cube [tex]= 8*6*4[/tex]
[tex]= 192 cm^3[/tex]
To create the X as the sides of the cube we should add material.
The nearest cube number to 192 exists at 216
The amount of material to be added exists
= 216 -192
[tex]= 24 cm^3[/tex]
The minimum volume of molten metal which should be added to mold It into a cube exists [tex]$24 cm^3[/tex].
Therefore, the correct answer is an option (4) 24.
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Rachel is getting a sundae where the cost is proportional to the weight of the sundae she makes. last time rachel went she bought a 12-ounce sundae for $4.20. this time she buys a 17-ounce sundae. let c be the cost of the sundae. set up and solve a proportion for c.
Using proportions, the cost of the 17-ounce sundae is of $5.95.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Considering the 12-ounce sundae bought for $4.2, the cost per ounce is given by the following proportion:
$4.2/12 = $0.35.
Hence the cost of a 17-ounce sundae is:
$0.35 x 17 = $5.95.
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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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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:
The roots of functions are approximately x =0 sec and x =9.8 sec the first root tell us that the height of arrow was 0 meters
The complete statements are:
The first root tells us that the height of the arrow was 0 meters above his bow after 0 seconds The second root says that it takes approximately 9.8 seconds for the arrow to return to the height of the bow. We can interpret our vertex to mean that at approximately 5 seconds at 120 metersHow to complete the blanks?The complete question is added as an attachment
The roots are given as:
x = 0 second
and
x = 9.8 seconds
x = 0 implies that the height of the arrow was 0 meters above his bow after 0 seconds
x = 9.8 implies that it takes approximately 9.8 seconds for the arrow to return to the height of the bow.
The x-value of the vertex is
x = (0 + 9.8)/2
Evaluate
x = 4.9
Approximate
x = 5
This means that the vertex is approximately 5 seconds
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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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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 =
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]
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
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]
*100 Points*
1. Joey decides to spin the wheel 60 times. What is the expected outcome of spins? (How many times should it land on each space?)
2. Use your information from question 1 to determine whether or not this wheel is profitable for the person who owns the booth. Explain your reasoning in full sentences.
3. What could the booth owner do to make the wheel more profitable for himself? You may include a drawing of the more profitable wheel if you would like. Explain your reasoning in complete sentences
Please help me whoever answers all three I will mark brainlest
The expected outcome of spins based on the probability information is 60.
How to calculate the probability?From the information, Joey decides to spin the wheel 60 times. Therefore, the expected outcome of spins is 60.
The thing that the booth owner can do to make the wheel more profitable for himself is to make winning probability less than that of losing.
Here, the booth owner do makes the wheel more profitable for himself as the winning is smaller.
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A taxi charges $2.50 for the first mile and $0.40 for each mile after that. The expression below shows how to find the total cost, in dollars, of a 20-mile taxi ride. 2.50 0.40 (20 minus 1)
The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.
Given a taxi charges $2.50 for the first mile and $0.40 for each mile
We are required to make an expression showing total cost and total cost of a 20 mile ride.
let the miles ride by tax be x.
Total cost of the product or service=Number of units*price of one units.
We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.
So,the expression showing looks like 2.50+0.40x.
Now to find the cost when taxi travels 20 miles, we have to put x=20,
Cost=2.50+0.40*20
=2.50+(40*20)/100
=2.50+800/100
=2.50+8
=$10.50
Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.
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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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A _______ group is another name for a command group
Answer:
department
Step-by-step explanation:
A "task force" group is another name for a command group.
We have,
A task force is a temporary grouping of individuals or units with a specific objective or mission.
It is typically formed to address a particular task or problem and is led by a designated commander or leader.
Task forces can be assembled from different departments or organizations to collaborate and work together towards a common goal.
Thus,
A "task force" group is another name for a command group.
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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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Sabrina finished 8/11 of her math assignment. if there are 22 problems in her assignment what fraction represents the number of problems completed over the total number of problems in the assignment ?
The fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.
According to the question,
There are 22 problems in her assignment and Sabrina finished 8/11 of her math assignment.
In order to find the fraction represents the number of problems completed over the total number of problems in the assignment.
(8/11) * (2/2) = 16/22
Hence, the fraction 16/22 represents the number of problems completed over the total number of problems in the assignment.
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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!
A die is rolled twice. What is the probability of getting either a multiple of 2 on the first roll or a total of 6 for both rolls
The correct answer is 7/12.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.Let A = Getting multiple of on the first one
B = A total of for both roll
P (A U B) = P(A) + P(B) - P(A ∩ B)
[tex]\frac{18}{36} + \frac{5}{36} - \frac{2}{36} \\\\ = \frac{21}{36} \\[/tex]
[tex]\frac{7}{12}[/tex]
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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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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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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
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?
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.
HELP ASAP PLS
Select the correct answer from each drop-down menu.
Quadratic function f is shown on the graph.
I don't know what the options are in the drop-down menu but the function f is symmetric around the point (4,–1) which is called the axis of symmetry. (4,–1) is the minimum of the graph.
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.
please help me to get an answer thanks
Answer:
A=P(1+in)
A=13000(1+6/100×9)
A=press calculator
A plot of land has been surveyed for a new housing development with borders AB, BC, DC, and DA. The plot of land is a right trapezoid with a height of 60 feet and an opposite leg length of 65 feet.
Right trapezoid A B C D is shown. Angles A and D are right angles. Sides A B and D C are parallel. The length of A D is 60 feet and the length of B C is 65 feet.
If the measure of angle BCD is 67.4°, the measure of angle ABC is
°.
If the length of base AB is 80 feet, the length of DC is
feet.
Answer:
90 approximately because if AB is 80 then DC should be 90 because AB come before DC in letters
Answer:
112.6 degrees and 105 feet.
Step-by-step explanation:
took the assignment
7. Jeff and Stephen go to the mall. The two
boys buy a total of 15 T-shirts. Stephen gets
three less than twice as many T-shirts as Jeff.
a) Write an equation to represent the
information in the second sentence.
b) Write an equation to represent the
information in the third sentence.
c) Solve the linear system by substitution
to find the number of T-shirts each boy
bought.
d) If the T-shirts cost $8.99 each, how
much did each boy spend before taxes?
Answer:
Let j = number of shirts Jeff bought and s = the number of shirts Stephen bought.
a.) s + j = 15
b.) 2j - 3 = s
c.) Plug 2j -3 into the equation from question a.
2j -3 + j = 15
3j -3 = 15
3j = 18
j = 6
2j - 3 = s when j = 6
2(6) - 3 = s
s = 9
Jeff bought 6 shirts; Stephen bought 9 shirts.
d.) Jeff cost = 8.99(6) = $53.94
Stephen cost = 8.99(9) = $80.91
90 pointssss!Please help! On parts a, b, and c. Thank you!
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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