Question 2
Answer:
Explanation:
Let x be a random variable representing the mean amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado. Given that it is normally distributed, we would calculate the z score by applying the formula,
z = (x - μ)/σ/√n
where
μ is the population mean
x is the sample mean
σ is the population standard deviation
n is the sample size
From the information given,
n = 40
x = 8.9
μ = 8.4
σ = 1.8
Thus,
z = (8.9 - 8.4)/(1.8/√40) = 1.76
We want to calculate P(x < 8.9). The probability value corresponding to z = 1.76 from the normal distribution table is 0.9608
Thus, the probability that their mean rebuild time is less than 8.9 hours is 0.9608
Figure ABCDE is similar to figure VWXYZ.Solve for the side length of WX.a 1/2b. 3c. 2.5 d 2
In similar figures the ratio of corresponding sides is the same:
Corresponding sides in given figure:
AB and VW
BC and WX
CD and XY
DE and YZ
EA and ZV
As you know the length of AE and ZV and need to find the value of WX taht is correspondig side of BC, you have the next:
[tex]\frac{ZV}{EA}=\frac{WX}{BC}[/tex][tex]\frac{4}{10}=\frac{WX}{5}[/tex]You use this equation to find the length of WX:
[tex]\begin{gathered} \frac{5\cdot4}{10}=WX \\ \\ \frac{20}{10}=WX \\ \\ \\ WX=2 \end{gathered}[/tex]Then, the length of WX is 24) A quart of liquid has a mass of 2.70 kilograms. How many quarts will take to weight 100 pounds?
We will have the following:
1)
[tex]10\operatorname{km}\cdot\frac{0.621mi}{1\operatorname{km}}=6.21mi[/tex]2)
[tex]\frac{14}{2}\frac{bales}{\text{week}}\cdot\frac{52\text{week}}{1\text{year}}=364\frac{bales}{\text{wek}}[/tex]3)
[tex]\frac{85.4\text{yard}}{5\min}\cdot\frac{1\text{min}}{60s}\cdot\frac{16\text{inch}}{1\text{yard}}\cdot\frac{2.54\operatorname{cm}}{1\text{inch}}\cdot\frac{1m}{100\operatorname{cm}}\approx0.1156885333\ldots\frac{m}{s}[/tex]4)
[tex]100lb\cdot\frac{1\operatorname{kg}}{2.2lb}\cdot\frac{1\text{quart}}{2.70\operatorname{kg}}=\frac{5000}{297}\text{quarts}\approx16.83501684\ldots quarts[/tex]***Screenshot***
Solve the following linear equation using equivalent equations to isolate the variable. Express youranswer as an integer, as a simplified fraction, or as a decimal number rounded to two places.2345 2----U43НЕ KeyAnswerHow to enter your answer (Opens in new window)Keyboard ShoU=
Given the equation
[tex]\frac{-3}{4}-\frac{2}{3}=\frac{5}{4}u-\frac{2}{3}u[/tex]We add and subtract similar terms:
[tex]-\frac{17}{12}=\frac{7}{12}u[/tex]Multiply both sides by 12:
[tex]\begin{gathered} -\frac{17}{12}\cdot12=12\cdot\frac{7}{12}u \\ -17=7u \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} -\frac{17}{7}=\frac{7u}{7} \\ u=-\frac{17}{7} \end{gathered}[/tex]Answer:
[tex]u=-\frac{17}{7}[/tex]construct the perpendicular bisectors of each side of the triangle. Extend the bisectors until they intersect each other.
Solution:
Given:
To draw the perpendicular bisector of each side, place the compass at the two ends of the line.
Using the line WX, expand the compass to beyond half of the line and place the compass at the first point (point W), to draw an arc above and below.
Then place the compass at the other point of the line (point X), and draw an arc to intersect the initially drawn arcs.
Join the two points of intersection to get the perpendicular bisector of the line.
Repeat the same for the other two sides to get the perpendicular bisectors.
Evaluate / Solve b3 + ac – bif a = 4, b=5, and c = 10.A.170B.165C.160D.125
Answer
Option C is correct.
The answer is 160.
Explanation
We are told to evaluate or solve
b³ + ac - b
if a = 4, b = 5 and c = 10
So, to solve, we will just substitute the given values into the expression to be solved
b³ + ac - b
= (5)³ + (4 × 10) - 5
= 125 + 40 - 5
= 160
Hope this Helps!!!
can someone please help me find the valu of X
Two triangles than make the whole triangle are proportional then
[tex]15\longrightarrow30[/tex]and the upper side of the left triangle is x
we can calculate the lenght of upper triangle
[tex]36-15=21[/tex]then
[tex]21\longrightarrow x[/tex]we join the relations
[tex]\begin{gathered} 15\longrightarrow30 \\ 21\longrightarrow x \end{gathered}[/tex]we use cross-multiplication. The product of 21 by 30 dividing between 15 is equal to x
[tex]\begin{gathered} x=\frac{21\times30}{15} \\ \\ x=42 \end{gathered}[/tex]the value of x is 42 units
Find the area of the figure. Remember to label use ^2 for units squared.10 ft15 ftA=12 ft
Solution
Find the area of the figure.
Area of the figure : Area of a parallelogram = base x height
base = 15ft
height = 10ft
[tex]\begin{gathered} A=bh \\ A=(15\times10)ft^2 \\ A=150ft^2 \end{gathered}[/tex]Therefore the area of the figure = 150ft²
is it possible for a rhombus to have a angle of 120 degrees and a angle of 30 degrees ? homework question
Solution:
From the properties of a Rhombus;
Opposite angles of a rhombus are equal.
The adjacent angles of a rhombus are supplementary, i.e. adds up to 180°
If one of the angles of a rhombus 120°, and the sum of the adjacent angles is 180°, then, the adjacent angle will be 60° (180° - 120° = 60°)
If one of the angles of a rhombus is 30°, then, the adjacent angle will be 150° (180° - 30° = 150°)
Thus, the sum of 120° and 30° is not supplementary and definitely can not be adjacent, since they do not sum up to 180°.
Hence, it is not possible
Which expression is equivalent to 6c^2d^5/2c-2c^10/d^-2 ? A. 8c^11d^3B. 5c^13d^7C. 6c^11d^7D. 6c^12d^3
Sam has $4.30 in quarters and nickels. He has 26 coins in all. The following system of equations can be used to represent this situation. 0.25q +0.05n = 4.30 q+n=26 What does the solution to the system (q, n) represent? (4 pts.) A.There is not enough information to determine. B.The value of the quarters and nickels Sam has C.The number of quarters and the number of nickels Sam has. D.The total amount of money Sam has.
ANSWER
C.The number of quarters and the number of nickels Sam has.
EXPLANATION
We have that the system of equations representing the situation is:
0.25q + 0.05n = 4.30
q + n = 26
The solution to the system of equations (q, n) will represent the number of quarters and nickels that Sam has.
This is because the sum of q and n is 26 and we are told that Sam has 26 coins.
Therefore, we can conclude that (q, n) represents the number of quarters and nickels that Sam has.
Designing Doorways for Rich and RizPON D5512ProblemRich has plenty of space abovenstead in this may Rizis quite a bitWat het oude budhat would give the same amount ofhadicom proportionatasRepen555sony net 50
Step 1
Calculate the difference in Rich height and the height of the doorway
6' 67/100'' - 5 5 3/4''
= 1' 19/100''
Then add the difference to Riz height
1' 19/100'' + 6' 8 1/2''
= 7' 9/10''
The height of the doorway that would give Riz enough space is 7' 9/10''
What is the acceleration of a 50 kg object pushed with a force of 500 newtons?10 m/s225,500 m/s2490 m/s225 m/s2
Let's use Newton's second law of motion:
F = m*a
Where:
F= Force = 500
m = mass = 50
a = acceleration
So:
500 = 50*a
Solve for a:
Divide both sides by 50:
500/50 = 50a/50
10 = a
a = 10m/s²
A real estate agent earned $1,625 for selling a property. If his commission rate is 5%, find the selling price of the property.
Let x be the selling price of the property, then we know that the 5% of x is $1,625.
Now, recall that the n% of an amount can be computed by multiplying the amount by
[tex]\frac{n}{100}\text{.}[/tex]Therefore:
[tex]x\times\frac{5}{100}=1625.[/tex]Solving the above equation for x, we get:
[tex]x=\frac{1625\times100}{5}\text{.}[/tex]Simplifying the above result, we get:
[tex]x=32500.[/tex]Answer:
[tex]32500[/tex]dollars.
Lesson 6: Relate Division and Multiplication Cool-down: A Different Relay Race 1. Lin and Han ran a 5 mile relay race as a team. They each ran the same distance. Dras diagram to represent the situation.
Lin and Han ran a 5 miles relay race.
If they both ran same distance, that means each of them ran;
[tex]\frac{1}{2}(5\text{miles)}=2.5\text{miles}[/tex]So, Lin and Han ran 2.5miles each.
The diadramatic representation of this scenario is;
The image above shows a track race of 5 miles divided into two. LIN ran half of it (2.5 miles) and also Han ran the other half, also (2.5 miles)
kareem correctly answered 85% of the questions on his math test. He missed 6 questions. How many questions were on his test
Answer:
40 questions
Explanation:
The total number of questions on his test represents 100%.
So, If he correctly answered 85% of the questions, then he missed 15% of the questions because:
100% - 85% = 15%
Therefore, 15% of the questions are equivalent to 6 questions, then we need to find the number equivalent to 100%. So 100% is equivalent to:
[tex]100\text{ \% }\times\frac{6}{15\text{ \%}}=40[/tex]Then, there were 40 questions on his test.
Is AABC= ADEF? If so, name the postulate that applies.AGiven:ŁAZDZBZE
Step 1:
Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles.
Step 2:
If the three angles (AAA) are congruent between two triangles, that does NOT mean that the triangles have to be congruent.
Final answer
Option A
Might not be congruent.
6cmA bakery sells hollow chocolate spheres. The larger diameter of eachsphere is 6 cm. The thickness of the chocolate of each sphere is 0.65 cm.Part A: What is the amount of chocolate in each hollow sphere? Stateyour answer to the nearest tenth of a cubic centimeter.o
As given by the question
There are given that the larger diameter of each sphereis 6 cm.
Now,
(A).
From the formula of volume:
[tex]V=\frac{4}{3}\pi\times r^3[/tex]Then,
[tex]\begin{gathered} V=\frac{4}{3}\pi\times r^3 \\ V=\frac{4}{3}\pi\times(3)^3 \\ V=\frac{4}{3}\pi\times27 \\ V=4\pi\times9 \\ V=113.097 \end{gathered}[/tex]Now,
From the formula without thickness:
[tex]\begin{gathered} V=\frac{4}{3}\times\pi\times r^3 \\ V=4\times\pi\times1.5 \\ V=18.8495 \end{gathered}[/tex]Then,
[tex]\begin{gathered} V=113.097-18.8495 \\ V=94.2475 \\ V=94.2cm^3 \end{gathered}[/tex]Hence, the volume of chocolate is 94.2 cm^3.
emily bought a pair of headphones on sale, if they usually cost 36.80, and emily purchased them at 40% how much did she pay? PLEASE GIVE ME A STEP BY STEP EXPLANATION PLEASE
Emily will pay $22.08 to buy the headphones after the discount of 40%.
Define percentage discountWhen a product is offered at a discount, the seller is reducing the product's price from what it was originally listed for. The percentage discount on the product is determined by the discount amount stated as a percentage of the original price.
Given data -
Cost of headphones - $36.80
Total price of product is considered as a 100%.
As Emily purchased them at 40%, she should be paying 60% of the amount.
Therefore, the amount she is paying to buy the headphones
= 60% of $36.80
= [tex]\frac{60}{100}[/tex] * $36.80
= 0.6 * $36.80
= $ 22.08
Emily will pay $22.08 to buy the headphones.
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A certain paint mixture weighing 300 lb contains 20% solids suspended in water. How many pounds of water must be allowed to evaporate to raise the concentration of solids to 22%?
27.27 lb of water must be allowed to evaporate
Explanations:Weight of the paint mixture = 300 lb
The paint mixture contains 20% solids suspended in water
Weight of solids suspended in water = (20/100) x 300
Weight of solids suspended in water = 60 lb
Let the weight of the mixture after evaporation be w
[tex]\begin{gathered} \frac{22}{100}\times w\text{ = 60} \\ 0.22w\text{ = 60} \\ w\text{ = }\frac{60}{0.22} \\ w\text{ = }272.73\text{ lb} \end{gathered}[/tex]The weight of the mixture after evaporation = 272.73lb
The weight of water that will be allowed to evaporate = 300 lb - 272.73 lb
The weight of water that will be allowed to evaporate = 27.27 lb
Therefore, 27.27 lb of water must be allowed to evaporate
Convert 77.6% to an
equivalent decimal.
Answer:
Step-by-step explanation:
0.776 in decimal form.
Ciara has a bag of 50 colored marbles. There are yellow, green, and white marbles. She empties the bag, sorts the marbles, and counts11 yellow marbles and 19 green marbles. She wants to write a ratio of the number of green marbles to the number of white marbles. How can she find the number ofwhite marbles without counting them?
The total number of marbles is, 50.
11 yellow marbles
19 green marbles
x be the number of white marbles.
Without counting, x can be calculated as,
[tex]\begin{gathered} 11+19+x=50 \\ x=50-11-19=20 \end{gathered}[/tex]Therefore the ratio of green marbles to white marbles is,
[tex]\frac{G}{W}=\frac{19}{20}[/tex]Thus option B is correct.
Given 8 x = 2 y - z, solve for y if x 2 and z = 2.
Answer
y = 9
Explanation
The question wants usto solve for y, given that
8x = 2y - z
if x = 2 and z = 2
To solve this, we just substitute the given values for x and z into the given expression to get y.
8x = 2y - z
8(2) = 2y - 2
16 = 2y - 2
We can rewrite this and have
2y - 2 = 16
Add 2 to both sides
2y - 2 + 2 = 16 + 2
2y = 18
Divide both sides by 2
(2y/2) = (18/2)
y = 9
Hope this Helps!!!
Convert: 3120 millimeters =centimeters
Given 1 centimeter = 10 milimeters.
To convert a number in millimeters into centimeters, divide the number by 10.
[tex]\begin{gathered} 3120millimeters=\frac{3120}{10}centimeters \\ =312centimeters \end{gathered}[/tex]Answer: 312 centimeters.
The correct answer is 2 and 5 only please explain why tho
We have that the graph has inflection points where the slope of the function is "0".
From this function we can see that the slope is "0" when x = 2 & x = 5; in all other places the slope is different from "0".
PLEAS WILL GIVE BEST RATE OR BRANILEST NEED HELP ASAP
Given figure is of a quadrilateral, with four sides.
We have, the sum of all the interior angles in a quadrileteral is 360.
Thus, we have,
[tex]80+95+38+x=360[/tex]Solving for x, we have,
[tex]\begin{gathered} x+213=360 \\ x=360-213=147 \end{gathered}[/tex]Thus, x = 147.
Which of the following graphs represents the equation 3x + 2y = 24?
Answer:
C
Step-by-step explanation:
if x=0
2y = 24
2/2 y = 24/2
y = 12
if y =0
3x = 24
3/3 x = 24/3
x = 8
2 3/4 divided by 10
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
The quotient is 11/40.
What is a mixed number?It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.
2 3/4= 11/4
11/4 is divided by 10 then,
It becomes 11/40
So, the quotient is 11/40
Here, 11/40 cannot be converted into a mixed number.
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Julian has a hundred songs on his media player he knows that 1/4 of the song or Jazz and the rest are pop which statement correctly describes the song on Julian media player
100 songs
1/4 of those are Jazz songs and the rest 3/4 are Pop songs
1/4=0.25
3/4=0.75
To know how many Jazz songs are multiply 100*0.25= 25 Jazz songs
Pop songs: 100*0.75= 75 pop songs
If Matthew rolls a number cube 90 times, how many times can he expect it 2 poilto land on an odd number?
Solution
The total face of a cube is 6
Possible odd 1,3,5
[tex]Probability\text{ =}\frac{Possible\text{ outcome}}{Total\text{ outcome}}[/tex]The cube is numbered one through six, and the odd numbers are therefore 1,3,5. So the probability of rolling an odd number in any given single roll is
[tex]\frac{3}{6}=\frac{1}{2}[/tex]Multiplying this probability by the number of times she rolls the cube gives
[tex]\frac{1}{2}\times90=45[/tex]The final answer
[tex]45[/tex]Find the vertex of the quadratic function below. Write your answer in fractional form if necessary. Do not use decimals.
Given quadratic expression is
[tex]f(x)=-3x^2-4x+7[/tex]Comparing with the general quadratic function
[tex]f(x)=ax^2+bx+c[/tex]We have,
[tex]a=-3,b=-4,c=7[/tex]So, the x coordinate of the vertex is
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{-4}{-6} \\ =-\frac{2}{3} \end{gathered}[/tex]Now, putting the x coordinate in the equation of the given function,we have,
[tex]\begin{gathered} f(-\frac{2}{3})=-3(\frac{4}{9})-4(-\frac{2}{3})+7 \\ =-\frac{12}{9}+\frac{8}{3}+7 \\ =\frac{75}{9} \end{gathered}[/tex]So, the vertex of th egiven quadratic function is at
[tex](-\frac{2}{3},\frac{75}{9})[/tex]