Grape juice comes in a 64 oz bottle. Apple juice comes in a 80 ounce bottle. Both juices will be poured into cups of equal size so that no juice remains in either bottle. How many ounces is the largest possible cup that can be used for both juices?
Which graph represents the solutions to the inequality |2x − 4| less than or equal to 14?
A)number line with an open circle on negative 5, shading to the right and an open circle on 9, shading to the left
B) number line with a closed circle on negative 5, shading to the right and a closed circle on 9, shading to the left
C) number line with an open circle on negative 5, shading to the left and an open circle on 9, shading to the right
D) number line with a closed circle on negative 5, shading to the left and a closed circle on 9, shading to the right
Exactly 1/20 of the students in mr.perez's class has a bird. what percentage of his students has a bird.
a study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 chevrolet cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 64 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.6 hours
Since we know the population standard deviation and the sample size is above 30, then we use the z statistic. The formula for z score is:
z = (x – u) / s
where,
x = the sample mean or sample value = 8.6 hours
u = the population mean = 8.4 hours
s = the standard deviation = 1.8 hours
Substituting into the given equation:
z = (8.6 – 8.4) / 1.8
z = 1.11
Using the standard probability distribution tables for z, a value of z = 1.11 has a probability of:
p = 0.8665
However this is still not the correct answer since this refers to the left of z. What we are trying to find is to the right of z since problem ask for exceeds 8.6 hours, therefore the correct answer is:
P (x>8.6 hours) = 1 – 0.8665
P (x>8.6 hours) = 0.1335
Therefore there is a 13.35% chance that the mean rebuild time is greater than 8.6 hours.
An electronic product contains 40 integrated circuits. the probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. the product operates only if there are no defective integrated circuits. what is the probability that the product operates?
Final answer:
The probability that the product operates is 0.6706 or 67.06%.
Explanation:
To find the probability that the product operates, we need to find the probability that all 40 integrated circuits are not defective. Since the probability of any integrated circuit being defective is 0.01, the probability that a circuit is not defective is 1 - 0.01 = 0.99. Since the integrated circuits are independent, we can multiply the probabilities together:
P(product operates) = (0.99)⁴⁰ = 0.6706
Therefore, the probability that the product operates is 0.6706 or 67.06%.
This only has one solution and I needz some halp with this. f - 6 = f + 8
the point(-2,4) is on the line given by the equation below
A.y=x -4
B.y=x+4
C.y=2x
D.y=-2x
If the slope of a straight line Is 0 and the y-intercept is -2, what is the equation of the line
it is simply y=-2
hoped I helped :)
In a recent local taste contest testing Coke against Pepsi it was found that 3/5 of all people surveyed preferred to taste the Coke. if 7,500 people were in the survey how many chose Pepsi ?
Answer: 3,000
Step-by-step explanation:
Given : In a recent local taste contest testing Coke against Pepsi it was found that [tex]\dfrac{3}{5}[/tex] of all people surveyed preferred to taste the Coke.
If 7,500 people were in the survey , then the number of people chose coke will be :-
[tex]\dfrac{3}{5}\times7500=3\times1500=4500[/tex]
Now, the number of people chose Pepsi = 7,500-4,500=3,000
Hence, there are 3,000 people who chose Pepsi.
Mix 20ml per 500 ml of water what is ratio of the amount of insecticide to the amount of water
Answer:
1 : 25
Step-by-step explanation:
Mix 20 ml per 500 ml. of water the ratio is = 20 : 500
Or [tex]\frac{20}{500}[/tex] = [tex]\frac{1}{25}[/tex] = 1 : 25
1 ml insecticide per 25 ml of water.
The ratio of the amount of insecticide to the amount of water is 1 : 25
Fractions are written as the ratio of two integers. The ratio of the amount of insecticide to the amount of water is 1:25
Ratio and proportionsFractions are written as the ratio of two integers
From the given question, we have the following measurement:
20ml per 500 ml of water
Required
The ratio of the amount of insecticide to the amount of water
Ratio = 20ml/500ml
Ratio = 1/25 = 1:25
Hence the ratio of the amount of insecticide to the amount of water is 1:25
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What is the distance between the two points?
is okay you lease a car at $415 per month for 4 years estimate the total cost of the least
The total cost of the least is $19,920.
Here,
lease a car at $415 per month for 4 years.
We have to find the total cost of the least.
What is Multiplication?
Multiplication is the process of calculating the total of one number multiplied by another.
Now,
lease a car at $415 per month for 4 years.
1 years = 12 month
4 years = 4 x 12 = 48 months.
Hence, total cost of the least = $415 x 48
= $19,920
So, The total cost of the least is $19,920.
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The difference between the squares of two numbers is 7. four times the square of the first number increased by the square of the second number is 73. find the numbers.
The difference between the squares of two numbers is 7. Four times the square of the first number increased by the square of the second number is 73. By formulating this information into equations, the numbers, thus, obtained are 3 and 4 or -3 and -4.
An equation is a combination of numbers, variables, functions, mathematical operations, etc. in a meaningful way. The equation comprises two or more expressions separated by the equality sign(=), indicating the equivalency.
Let the numbers be x and y, then according to the question,
[tex]x^2 - y^2 = 7[/tex] ...(i)
[tex]4x^2 + y^2 = 73[/tex] ...(ii)
Add both equations,
[tex](x^2 - y^2) + (4x^2 + y^2) = 7 + 73\\(x^2 + 4x^2) + (-y^2 +y^2) = 80\\5x^2 = 80\\x^2 = 16\\x = \pm4[/tex]
Put x = 4 in equation (i),
[tex]4^2 - y^2 = 7\\16 - y^2 = 7\\y^2 = 16-7\\y^2 = 9\\y = \pm3[/tex]
So, the numbers are 3 and 4 or -3 and -4.
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A single person earns a gross biweekly salary of $780 and claims 6 exemptions. What is the person's net pay?
a.
It is the same as the gross pay.
b.
It is $11 more than the gross pay.
c.
It is $11 less than the gross pay.
d.
It is $13 less than the gross pay
Answer:
A. It is the same as the gross pay.
Explanation:
To get the amount of income tax withheld, we use the table attached.
We are given that:
1- This biweekly gross salary is $780, therefore, we will go to the row having a minimum payment of $780 (red border)
2- The number of claimed allowances is 6, therefore, we will go to the column with 6 claimed allowances (blue border)
We now find the intersection between the row and the column. As we can see in the table, it is zero.
This means that the deducted taxes based on the givens is zero which means that the net pay is the same as the gross pay.
Hope this helps :)
Final answer:
To calculate the net pay, deduct the taxes and other deductions from the gross salary. Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay.
Explanation:
To calculate the net pay, we need to deduct the taxes and other deductions from the gross salary. The main deductions to consider are Social Security, Medicare, and federal and state taxes. Let's break it down.
Calculate Social Security deduction: Gross biweekly salary x 6.2%.Calculate Medicare deduction: Gross biweekly salary x 1.45%.Calculate federal and state taxes: Gross biweekly salary x 15%.Add up all the deductions.Subtract the total deductions from the gross salary to find the net pay.
Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay. Therefore, the correct answer is option c. $11 less than the gross pay.
A square is inscribed in a circle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
The probability of the point will be in the shaded region is 0.64 or 64%.
A square is inscribed in circle. Probability of point to be pick from the square to be find out.
Venn diagram are the Figures of probabilities to understand better.
Here, diameter of circle = d and radius r =d/2, edge of the square = a
By Pythagorean theorem,
a²+a²=d²
2a²= (2r)²
a²=2r²
Area of the square =2r²
Area of the circle = πr²
Now probability = Area of the square/Area of the circle
= 2r²/πr²
= 2/π
= 0.64
Thus, The probability of the point will be in the shaded region is 0.64 or 64%.
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I need help badly please help !!
A ship traveled at an average rate of 22 miles per hour going west. It then traveled at an average rate of 12 miles per hour heading north. If the ship traveled a total of 158 miles in 9 hours, how many miles were traveled heading north?
the primary advantage of a stratified random sample is that it ____.
A pilot can fly an airplane 2240 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 40 mph, find the speed of the plane in still air.
Quadrilateral STWR is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary. Circle Q is shown with an inscribed quadrilateral labeled RSTW.
Answer:
Step-by-step explanation:
Arc STR measures twice the measure of angle R, and arc WRS measures twice the measure of angle T.
STR = 2 x ∠R and WRS = 2 x ∠T --- This is because of the Inscribed Angle Theorem
If the measure of arcs STR and WRS are added together, the total would be 360° since a full circle is made up of 360°.
So mSTR + mWRS = 360°
Substituting the angle measures of R and T in for the arcs, the equation becomes:
2 • ∠R + 2 • ∠T = 360°
Simplifying further:
2 • [∠R + ∠T] = 360°
∠R + ∠T = 360° / 2
∠R + ∠T = 180° - This proves that opposite angles of a quadrilateral inscribed in a circle are supplementary.
Which one of the following pairs of terms is composed of like terms? A. 2a, 2b B. –3x, +3y C. abc, cab D. 4mn, 3my
Answer:
Option C
Step-by-step explanation:
We have to find the pair of terms composed of like terms.
(A) 2a, 2b Unlike terms
(B) -3x, +3y Unlike terms
(C) abc, cab
As we know cumulative property of multiplication shows a×(b×c) = (a×b)c
Therefore, both the terms abc and cab are similar.
(D) 4mn, 3my Unlike terms
Option C is the answer.
Find AB if BC = 4 , BD = 5, and AD =4
A bag contains 6 poker chips, one is red and the other 5 are blue. you and a friend take turns selecting a chip at random from the bag. the first person to get the red chip is the winner. find the probability that you win if you go first and
Final answer:
The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.
Explanation:
The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.
If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:
P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...
This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:
P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.
Scotty is planning to order 1 cubic yard of topsoil for his 15' by 24' garden expecting that if evenly spread, he would end up with 2 inches of topsoil. Is he correct? Explain.
2 inches = 0.1666 feet
15 x 24 x 0.1666 = 59.98 cubic feet
1 cubic yard = 27 cubic feet
59.98 is greater than 27 so 1 cubic yard of topsoil will not be enough
Convert r =-72/12+6 sin theta to Cartesian form.
Answer:
The answer is b. [tex]4x^2+3y^2-24y-144=0[/tex]
Step-by-step explanation:
The equation is:
[tex]r=\frac{-72}{12+6\sin(\theta)}[/tex]
Cross multiply;:
[tex]r(12+6\sin(\theta)=-72[/tex]
Expand;:
[tex]12r+6r\sin(\theta)=-72[/tex]
Divide through by 6;:
[tex]2r+r\sin(\theta)=-12[/tex]
[tex]2r=-12-r\sin(\theta)[/tex]
Substitute;:
[tex]y=r\sin(\theta), r=\sqrt{x^2+y^2}[/tex]
[tex]2\sqrt{x^2+y^2}=-12-y[/tex]
Square both sides;:
[tex](2\sqrt{x^2+y^2})^2=(-12-y)^2[/tex]
[tex]4(x^2+y^2)=144+24y+y^2[/tex]
[tex]4x^2+4y^2=144+24y+y^2[/tex]
Simplify;:
[tex]4x^2+3y^2-24y-144=0[/tex]
What is the slope of a trend line that passes through the points (–3, 3) and (18, 26)?
Answer:
C.) 23/21
Step-by-step explanation:
just took the test on edge
The points L(10,9) M(10,-5) N(-1,-5) and O(-1,9) form rectangle L M N O Which point is halfway between O and N.
A.) (-1,0)
B.) (-1,7)
C.) (-1,2)
D.) (2,-1)
Answer:
C.) (-1, 2)
Step-by-step explanation:
You can plot the points on a graph, or you can just find the midpoint:
midpoint = (O + N)/2 = ((-1, 9) +(-1, -5))/2 = (-1-1, 9-5)/2 = (-2, 4)/2
midpoint = (-1, 2)
A company that packages cold cuts needs to transport the packaged meat to the supermarket.it will cost $1,200 to rent a truck,and it will cost an additional $100 for every 50 pounds transported.which equation represents the transport cost for every 50 pounds if cold cuts transported? The options are
A) y=1,200-100x
B) y= 1,200+100x
C) y=1,200x +100
D) y=100x-1,200
it to calculate the cost of $100 for every 50lbs, you would use 100x
then you need to add that to the 1200
so the equation would be y = 1200+100x
B is the correct answer
Find the volume of this figure to the nearest whole number. Use 3.14 for pi. Please help me!!
volume of square middle = 12 x 12 x 7 = 1008
if you put the 2 ends together it would be a cylinder so volume for that is:
3.14 x 6^2 x 7 = 791.28
1008 + 791.28 = 1799.28 round it off to 1800 mm^3
So D is the correct answer
Answer:
4th option is correct.
Step-by-step explanation:
Here in the given image, we can see that there can be 2 figures if separated. A cuboid with dimensions 12*12*7 and a cylinder with radius as 6 mm and height as 7 mm.
We will first find the volume of cuboid.
V = [tex]12\times12\times7[/tex] = 1008 cubic mm
Now, volume of cylinder is given as : [tex]\pi r^{2} h[/tex]
[tex]3.14\times6^{2}\times7[/tex] = 791.28 cubic mm
Now adding both the volumes to get the volume of complete figure:
V = [tex]1008+791.28=1799.28[/tex] cubic mm
Now this value is closest to option 4th : 1800 cubic mm.
Therefore, last option is true.
A Square has sides that are the same length as the radius of a circle. If the circle has an area of 36π square units how many units long is the perimeter of the square?