Based on the given coordinate grid, and the increment for each grid line, the coordinates of point A is ( fraction negative 1 and 1 over 4, fraction 3 over 4) or (-1¹/₄, ³/₄).
What are point A's coordinates?
The x-value of point A is said to be 5 grid lines to the left of y-axis. This means that the x value will be negative.
The increments are 1/4 so the x-value is:
= -1/4 x 5
= -1¹/₄
The y-value is given by the 3 grid lines above the x-axis which means that this value is positive:
= 1/4 x 3
= 3 /4
The coordinates of A are:
(-1¹/₄, ³/₄)
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The perimeter of a rectangular field is 282 yards. If the width of the field is 52 yards, what is its length?
Answer: 89 yards
Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.
Answer:
75
Step-by-step explanation:
math
thank you for helping
Please help! I don't understand how to solve this problem
Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.Assuming an uniform distribution, the standard deviation is given by:
[tex]S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size is found solving for n when the margin of error is of M = 0.006, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.006 = 1.96\frac{1.1547}{\sqrt{n}}[/tex]
[tex]0.006\sqrt{n} = 1.96 \times 1.1547[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2[/tex]
n = 142,282.
A sample of 142,282 should be taken, which is not practical as it is too large of a sample.
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A right triangle has a base of 8 1/2 inches and a height of 12 1/2. If the height is reduced to 4 inches, how many inches is the new base?
The length of the new base is 26.56 inches or [tex]26\frac{14}{25}[/tex] inches. Using the area of a right triangle, the required base is calculated.
How the area of a right triangle is calculated?The area of the right triangle is given by
A = [tex]\frac{1}{2}[/tex] × b × h sq. units
Where A -area; b -base; h -height;
Calculation:It is given that,
The right triangle has a base of length b = 8 1/2 = 8.5 inches and a height of length h = 12 1/2 = 12.5 inches.
So, its area is
A = [tex]\frac{1}{2}[/tex] × 8.5 × 12.5 = 53.125 sq. inches
When the height of the right triangle is reduced to 4 inches,
53.125 = [tex]\frac{1}{2}[/tex] × b × 4
⇒ b = 53.125/2
∴ b = 26.56 or [tex]26\frac{14}{25}[/tex] inches
Thus, the length of the new base is 26.56 or [tex]26\frac{14}{25}[/tex] inches.
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Service Department Charges and Activity Bases
Middler Corporation, a manufacturer of electronics and communications systems, uses a service department charge system to charge profit centers with Computing and Communications Services (CCS) service department costs. The following table identifies an abbreviated list of service categories and activity bases used by the CCS department. The table also includes some assumed cost and activity base quantity information for each service for October.
CCS Service
Category
Activity Base
Budgeted Cost Budgeted Activity
Base Quantity
Help desk Number of calls $160,000 3,200
Network center Number of devices monitored 735,000 9,800
Electronic mail Number of user accounts 100,000 10,000
Smartphone support Number of smartphones issued 124,600 8,900
One of the profit centers for Middler Corporation is the Communication Systems (COMM) sector. Assume the following information for the COMM sector:
• The sector has 5,200 employees, of whom 25% are office employees.
• All the office employees have been issued a smartphone, and 96% of them have a computer on the network.
• One hundred percent of the employees with a computer also have an e-mail account.
• The average number of help desk calls for October was 1.5 calls per individual with a computer.
• There are 600 additional printers, servers, and peripherals on the network beyond the personal computers.
a. Determine the service charge rate for the four CCS service categories for October.
CCS Service Category Service Charge Rate
Help desk $fill in the blank 1
Per call
Network center $fill in the blank 3
Per device monitored
Electronic mail $fill in the blank 5
Per user or e-mail account
Smartphone support $fill in the blank 7
Per smartphone issued
b. Determine the charges to the COMM sector for the four CCS service categories for October.
October charges to the COMM sector
Help desk charge $fill in the blank 9
Network center charge $fill in the blank 10
Electronic mail charge $fill in the blank 11
Smartphone support charge $fill in the blank 12
Feedback Area
Feedback
a
The answers to the question are:
50751014a. How to determine the service charge rate for the month of OctoberThis is the number of calls for the help desk
160000/3200 = 50per call
network center
735000/9800
= 75 per device that was monitored
Electronic mail
100000/10000 =
10 for the mail account
For smart phone support
124600/8900
= 14 per phone extension
b. Charges to the COMM sectorfor helpdesk
5200 * 0.25 * 0.96 *1.5 calls * $50
= 93600
For network center
(5200 * 0.25 * 0.96) + 600] x 75
= 138600
For Electronic mail
5200 * 0.25 * 0.96 * 10 per email account
= 12480
Smart support charge
5200 * 0.25 * 14 = 18200
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Help me with this question asap!
Answer:
false
Step-by-step explanation:
The converse of the statement is
If two angles are not a linear pair of angles, they are not adjacent.This is false by definition.
Please help due today. (43/7÷ x+32/9) ÷25/6=4/3
The solution to the equation as given in the task content is; x = -3.47.
What is the solution of the equation in discuss?It follows from the task content that the equation given is; (43/7÷ x+32/9) ÷25/6=4/3
(43/7÷ x+32/9) = 25/6 × 4/3
(43/7÷ x+32/9) = 100/18
x +32/9 = 43/7 ÷ 100/18
x + 32/9 = 774/700
x = 774/700 - 32/9
x = -3.47.
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Name the set(s) to which each number belongs.*
-20√/10
*More than one answer may be correct mark all correct answers.
A. reals
B. whole
C. integer
D. rationals
E. irrationals
F. natural
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The given number is :
[tex]\qquad❖ \: \sf \: \cfrac{ - 20}{ \sqrt{10} } [/tex]
since 10 isn't a perfect square, root 10 is an irrational number, and therefore the whole number is irrational as well, and we already know that irrational numbers are also part of real numbers.
[tex] \qquad \large \sf {Conclusion} : [/tex]
So the Correct choices are :
A. RealE. IrrationalWhat is the measure of
angle x?
Enter your answer in the box.
X =
Answer:
x = 48°
Step-by-step explanation:
Complementary angles
Angles that sum to 90°.
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Therefore, angle x is equal to the angle that is complementary to 42°.
To find x, subtract 42° from 90°:
⇒ x = 90° - 42°
⇒ x = 48°
Suppose each edge of the cube shown in the figure is 10 inches long. Find the sine and cosine of the angle formed by diagonals DE and DG.
Check the picture below.
[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]
Find X:
J:58
K:70
L:111
M:121
Answer: 111
Step-by-step explanation:
Angles in a quadrilateral add to 360 degrees, so:
[tex]121+58+70+x=360\\\\x=111[/tex]
Answer:
111
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 360:
121 + 58 + 70 + x = 360 add like terms
249 + x = 360 subtract 249 from both sides
x = 111 is the measure of the angle represented with x
Select ALL expressions that have a value less than 9.
A
B
C
D
E
2
5.9 +
23
√10
2√21
55
2
√85-2√3
Answer:
What is this?
Can't understand anything!
Answer : what is this question?
Which best describes the composition of tranformations that maps ∆LMN to ∆L'M'N'. 0,0 is the center of the dilation in each choice.
A. a reflection over the line y=3 followed by a dilation of scale factor 2
B. a dilation of scale factor 2 followed by a dilation of scale factor 12
C. a dilation of scale factor 12 followed by a translation left 1 down 3
D. a dilation of scale factor 2 followed by a translation right 1 up 3
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
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Identify an acute angle and give its measure.
Angle HEJ measures 15 degrees.
Given that mLa = 36° and m
Answer:
mLx = 144
mLy=154
Step-by-step explanation:
180-36=144
x=144
180-62=118
36+118=154
180-154=26
180-26=154
y=154
Answer:
154 degrees
Step-by-step explanation:
you can find measure of angle y, since it is the supplement of angle a, so
measure of angle y = 180 - measure of angle a, which is 144 degrees
you can find the measure of angle x, by finding its complement.
Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x
so, the supplement of angle x is 26 degrees, so x is 154 degrees
What is the measure of RCP?
Answer:
84
Step-by-step explanation:
15+15+27+27
the product of 6
and the sum of five
and a number
Answer:
6 * (5 + n)
Explanation:
Sum = addition
Difference = subtraction
Product = multiplication
Quotient = division
An insurance provider states that their customers save at least, on average, 300 dollars per year by switching to them, with a standard deviation of 150 dollars. Before we decide to switch to the new company and go through all of the hassle, we want to test the claim. So, we go out and sample 64 individuals who switched to the new insurance company and found them to have saved an average of 255 dollars per year. Do we have enough evidence at the α = 0.05 level to state that the insurance provider is false in their claim? Discussion Prompts Answer the following questions in your initial post: What are the hypotheses based on the words given in the problem? Should we use a Z or T distribution in this case? What is our Z or T statistic? What is the P-value? Based on your p-value and alpha, what conclusion will we make? Based on your results, would you switch to this company? Explain why or why not (Note: this can go beyond the use of statistics, but statistical analysis can help our decisions)
The solution to the question is mathematically given as
1)
H0: M [tex]\geqslant[/tex] 300
H0: M [tex]\geqslant[/tex] 300
2)
Z distribution.
3)
z=-2.4
4)
P=0.0082
5)
"H0" is rejected as a hypothesis with a level of significance of 0.05.
What is the hypothesis ?Generally, the equation for is mathematically given as
Solutions
we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]
(1):
H0: M [tex]\geqslant[/tex] 300 dollars; customers save at least 300 dollars per year by switching to them.
H0: M [tex]\geqslant[/tex] 300 dollars:
(This is a left-tailed test)
(2):
when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.
(3):
[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]
(4):
[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]
(5):
In conclusion, Since p-value = 0·0082 <0.05
This is statistically significant at the 0.05 level.
We thus "Refect H0" using a threshold of significance of 0.05.
"H0" is rejected as a hypothesis with a level of significance of 0.05.
There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.
Therefore, we would not consider making the transition to this firm.
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Write an expression involving exponents to represent the shaded area in square inches of the diagram than use that expression to calculate the shaded area in squares inches of the diagram
The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
Expression involving exponents and shaded areaThe expression is:
6²- (3² + 2²)
The shaded area:
Shaded area=6²- (3² + 2²)
Shaded area=36-(9+4)
Shaded area=36-13
Shaded area=23 square inches
Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
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Geometry and Modeling:
Mike completely filled the container shown below with 616 small cubes that were each [tex]\frac{1}{2}[/tex] inch long.
Part A: Calculate the volume of the prism.
Part B: Crate a graphical model of a prism with base 5.5 by 3.5 that has the same volume as Part A.
Show how Mike can calculate the volume of the prism, in cubic inches, by using a volume formula instead of filling the container with small cubes.
Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's
brother decides to join Hunter and leaves the house 30 minutes after him at a speed of
18 km/hr. How long will it take to Hunter's brother to catch up to him?
The time requires to catch up to him will be 3 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is a scalar quantity it does not require any direction only needs magnitude to represent.
Given that Hunter leaves his house to go on a bike ride. He starts at a speed of 15 km/hr. Hunter's brother decides to join Hunter and leaves the house 30 minutes after him at a speed of 18 km/hr.
The time will be calculated as below:-
30 minutes = 0.5 hour
15x = 18(x - 0.5)
15x = 18x - 9
-3x = -9
x = 3 hours
Therefore, the time requires to catch up to him will be 3 hours.
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Given the vertex of a quadratic function, find the axis of symmetry.
(i) The equation of the axis of symmetry is x = - 5.
(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
How to analyze and interpret quadratic functions
In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.
(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:
y = x² - 8 · x - 2
y + 18 = x² - 8 · x + 16
y + 18 = (x - 4)²
In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) Now here we must apply a procedure similar to what was in used in part (ii):
y = - 2 · (x² - 4 · x + 2)
y - 4 = - 2 · (x² - 4 · x + 2) - 4
y - 4 = - 2 · (x² - 4 · x + 4)
y - 4 = - 2 · (x - 2)²
According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
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HELP. Which statement best describes the domain of the function represented in the graph?
05 ≤x≤ 60, or x is from 5 to 60 05 ≤ x ≤ 30, or x is from 5 to 30 O 30 ≤ x ≤ 60, or x is from 30 to 60 00≤x≤ 30, or x is from 0 to 30
Factor the common factor out of 8^3 + 12x
The factorized expression of 8^3 + 12x is 4(128+ 3x)
How to factor the common factor out?The expression is given as:
8^3 + 12x
Evaluate 8^3
8^3 + 12x = 512 + 12x
Factor out 2 from the expression
8^3 + 12x = 2(256+ 6x)
Factor out 2 from the expression
8^3 + 12x = 2 * 2(128+ 3x)
Evaluate the product
8^3 + 12x = 4(128+ 3x)
Hence, the factorized expression of 8^3 + 12x is 4(128+ 3x)
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PLEASE HELP, TIMED
University students in an Iowa town have a mean hourly wage of $11.75, with a standard deviation of $1.25. The distribution of hourly wages is not assumed to be symmetric.
Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?
Round your answers to the nearest hundredth.
The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:
11.75 - 2 x 1.25 = $9.25.11.75 + 2 x 1.25 = $14.25.More can be learned about the Chebyshev Theorem at https://brainly.com/question/25303620
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Which expression is equivalent to (27.3 5.9)47
O 211.3-1.95
O228-(-3) 20.94
O 27.3-5.04
O228-3-20.94
The correct answer is Option 4.
if (a+10) and a are in straight line find the value of a
Answer:
a=170
Step-by-step explanation:
(a+10)=180[because being a straight line]
or, a+10=180
or,a=180-10
a=170
Therefore,a=170
(3a to 3rd power - 5b to 3rd power) + ? 3/a + ? b to the 3rd power = (3/a + b to the 3rd power)
The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
How to solve Algebraic Fractions?
We want to solve the algebraic fraction equation given as;
3a³ - 5b³ + (3/a) + b³
Rearranging the algebra to get;
(3a³ + (3/a)) + b³ - 5b³
Factorizing out 3/a and simplifying gives;
(3/a)(a⁴ + a) - 4b³
This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³
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If P(A)=12, P(A B)=16, and P(A B)=23, what is P(B)?
1/4
2/3
1/2
1/3
Answer:
P(B) 7
Step-by-step explanation:
The answer is P (B)
You have moved into a new house and your friends have come over to help paint the walls. Everyone paints at the same rate of 1.5 hours/wall.
QUESTION: If there are six people painting on Saturday, how many walls could you get painted in 3 hours?
walls
Answer:
12 walls
Step-by-step explanation:
Let's take everyone paints a different wall and there are no overlaps.
Given information from the question:
1.5 hours = 1 wall
1 hour =
[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]
per person.
From the information above, we can deduce:
6 people =
[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]
Since we know 6 people can paint 4 walls in an hour,
3 hours =
[tex]3 \times 4 \\ = 12 \: walls[/tex]
