A photograph having length of 24 inches which is proportionate to another photograph having dimensions 3 × 4 inches, has width of 18 inches.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
Let the width of the photograph be x inches.
The length of the photograph is 24 inches.
A similar proportion photograph has width as 3 inches.
A similar proportion photograph has length as 4 inches.
The equation to find the width of photograph is -
x / 24 = 3 / 4
Simplify the equation -
x = (24 × 3) / 4
x = 72 / 4
x = 18
Therefore, the width value is 18 inches.
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A city has a population of 350,000 peopleSuppose that each year the population grows by 7.75%What will the population be after 6 years Use the calculator provided and round your answer to the nearest whole number
Answer:
335%
Step-by-step explanation:
The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Assume that the population is normally distributed. Can we support, at the level of significance, the claim that the mean breaking strength has increased
The question is incomplete. The complete question is :
The breaking strengths of cables produced by a certain manufacturer have a mean of 1900 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 150 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1902 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased?
Solution :
Given data :
Mean, μ = 1900
Standard deviation, σ = 65
Sample size, n = 150
Sample mean, [tex]$\overline x$[/tex] = 1902
Level of significance = 0.01
The hypothesis are :
[tex]$H_0 : \mu = 1900$[/tex]
[tex]$H_1 : \mu > 1900$[/tex]
Test statics :
We use the z test as the sample size is large and we know the population standard deviation.
[tex]$z=\frac{\overline x - \mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{1902-1900}{65 / \sqrt{150}}$[/tex]
[tex]$z=\frac{2}{5.30723}$[/tex]
[tex]$z=0.38$[/tex]
Finding the p-value:
P-value = P(Z > z)
= P(Z > 0.38)
= 1 - P(Z < 0.38)
From the z table. we get
P(Z < 0.38) = 0.6480
Therefore,
P-value = 1 - P(Z < 0.38)
= 1 - 0.6480
= 0.3520
Decision :
If the p value is less than 0.01, then we reject the [tex]H_0[/tex], otherwise we fail to reject [tex]H_0[/tex].
Since the value of p = 0.3520 > 0.01, the level of significance, then we fail to reject [tex]H_0[/tex].
Conclusion :
At a significance level of 0.01, we have no sufficient evidence to support that the mean breaking strength has increased.
SCALCET8 3.9.013. A plane flying horizontally at an altitude of 2 mi and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station. (Round your answer to the nearest whole number.)
Answer:
DL/dt = 529 miles/h
Step-by-step explanation:
The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t point C) shape a right triangle wich hypothenuse L is:
L² = d² + x²
d is the constant distance between the plane and the ground
Then differentiation with respect to time on both sides of the equation
2*L*dL/dt = 2*d* Dd/dt + 2*x*dx/dt
But Dd/dt = 0
L*dL/dt = x*dx/dt
x = 5 miles dx/dt = 570 m/h L = √ d² + x² L √ (5)² + (2)²
L = √29 L = 5.39 m
5.39 *DL/dt = 5*570 m/h
DL/dt = 5*570/5.39 miles/h
DL/dt = 528.76 miles/h
DL/dt = 529 miles/h
It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles. Find its designed life if a .97 reliability is desired.
Answer:
The designed life should be of 21,840 vehicle miles.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.
This means that [tex]\mu = 35000, \sigma = 7000[/tex]
Find its designed life if a .97 reliability is desired.
The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 35000}{7000}[/tex]
[tex]X - 35000 = -1.88*7000[/tex]
[tex]X = 21840[/tex]
The designed life should be of 21,840 vehicle miles.
A little help?? It’s trig
Answer:
12 [tex]\pi[/tex] = 37.699 f/s
Actually, the more interesting question
would have been how fast is the ball going in MPH?
25.7 MPH
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2 [tex]* \pi * 1.2[/tex]
C = 2.4 [tex]\pi feet[/tex]
C (per second) = (5)(2.4 [tex]\pi feet[/tex])
C(per second) = 12 [tex]\pi[/tex] = 37.699 f/s
The sum of the angles of a triangle is 180. Find the three angles if one angle is twice the smallest angle and the third angle is 36 degrees greater than the smallest angle. Place them in order from least to greatest.
Answer:
36°, 72°, 72°Step-by-step explanation:
The angles are x, y and z:
x = 2y, z = y + 36Their sum is:
x + y + z = 1802y + y + y + 36 = 1804y = 144y = 36Then find the other angles:
x = 2*36 = 72z = 36 + 36 = 72Now we have to,
find the three angles if one angle is twice smallest angle and third angle is 36° greater than smallest angle.
Then take the values as,
→ smallest angle = x
→ y = 2x
→ z = x + 36°
Let we find the angles,
→ x + y + z = 180°
→ x + 2x + x + 36° = 180°
→ 4x = 180 - 36
→ 4x = 144
→ x = 144/4
→ [x = 36°]
Now the value of y is,
→ y = 2x
→ y = 2 × 36°
→ [y = 72°]
Then the value of z is,
→ z = x + 36°
→ z = 36° + 36°
→ [z = 72°]
Placing values from least to greatest,
→ 36°, 72°, 72°
Hence, the order is 36°, 72°, 72°.
Given: CD is an altitude of triangle ABC.
Prove: a^2 = b^2 +c^2 = 2bccos A
Answer:
Step-by-step explanation:
Statements Reasons
1). CD is an altitude of ΔABC 1). Given
2). ΔACD and ΔBCD are right 2). Definition of right triangles.
triangles.
3). a² = (c - x)² + h² 3). Pythagoras theorem
4). a² = c² + x² - 2cx + h² 4). Square the binomial.
5). b² = x² + h² 5). Pythagoras theorem.
6). cos(x) = [tex]\frac{x}{a}[/tex] 6). definition of cosine ratio for an angle
7). bcos(A) = x 7). Multiplication property of equality.
8). a² = c² - 2c(bcosA) + b² 8). Substitution property
9). a² = b² + c² - 2bc(cosA) 9). Commutative properties of
addition and multiplication.
PLEASE HELP ME PLEASE
Answer:
Ok so these triangle are the same with equivalent angles
so we can add up the angles 80+26=106
now we subtract from 180
180-106=74
so the measure of angle b is 74
Hope This Helps!!!
8) If 150% of a number is 75, then what is the 80% of that number?
A. 40
B. 50
C. 70
D. 85
Answer:
A. 40
Step-by-step explanation:
Answer:
A. 40
Step-by-step explanation:
75 ÷ 1.5 = 50 = original number
80% of 50 = 50 × 0.8 = 40
GM projected that 3% of their cars produced this year will be defective. If GM produced 1,698 cars that were defective, how many cars did GM produce this year
Answer:
56600 cars
Step-by-step explanation:
Below is the calculation of number of cars produced.
The percentage of cars that is defected = 3%
Number of cars that are defective = 1698 cars
The number of cars produced in a year = 1698 / 3%
The number of cars produced in a year = 56600 cars
A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than . Suppose that we suspect otherwise and carry out a hypothesis test. State the null hypothesis and the alternative hypothesis that we would use for this test.
Answer:
The null hypothesis is [tex]H_0: p \leq x[/tex], in which x is the proportion tested.
The alternative hypothesis is [tex]H_1: p > x[/tex]
Step-by-step explanation:
A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than x.
This means that at the null hypothesis, we test if the proportion is of at most x, that is:
[tex]H_0: p \leq x[/tex]
Suppose that we suspect otherwise and carry out a hypothesis test.
The opposite of at most x is more than x, so the alternative hypothesis is:
[tex]H_1: p > x[/tex]
Which of the following choices is the average speed of a tourist who traveled for 1 hour on a plane at 400 mph and 4 hours by car at 60 mph?
(average= total miles/total hours)
Answer:
128 mph
Step-by-step explanation:
1 hour = 400
4 hours = 240
240+400= 640
4+1 = 5
640/5=128
A map was created using the scale 1 inch :25
miles. If the river is 5.5 inches long on the map, then it is actually how many miles long?
what percentage of undergraduates students in Calculus 1 are required to do computer assignments in their classes
Full question:
Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used computer assignments. Suppose that 16% used both calculators and computers. a) What percent used neither kind of technology? b) What percent used calculators but not computers? c) What percent of the calculator users had computer assignments? d) Based on this survey, do calculator and computer use appear to be independent events? Explain.
Answer:
a. 34%
b. 35%
c. 31.4%
d. Independent events
Explanation:
a. To calculate percentage that used neither kind of technology, we already know those that use the technologies and total taking calculus so:
100%-51%-31%-16%= 34%
b. Percentage that used calculators but not computers.
= 51%-16%=35%
c. Percentage of the calculator users that had computer assignments?
= 16/51×100=31.4% (there are 16 people using both so that as a percentage of 51 people using calculators)
d. Independent events are events that do not affect the other, such that occurrence of one does not define occurrence of the other. Since percentage of calculator and computer assignment users is close to those who are not using any, we can say they are independent events.
A right rectangular prism has a length of 5 centimeters, a width of 8 centimeters, and a height of 4 centimeters. What is the volume of the prism?
Answer:
volume of prism is 160 cm
The scores on a psychology exam were normally distributed with a mean of 69 and a standard deviation of 4. What is the standard score for an exam score of 68?
The standard score is ?
Answer:
0.25
Step-by-step explanation:
Given that :
Mean score, μ = 69
Standard deviation, σ = 4
Score, x = 64
The standardized score, Zscore can be obtained using the formular :
Zscore = (x - μ) / σ
Zscore = (69 - 68) / 4
Zscore = 1 / 4
Zscore = 0.25
If one table and two lamps cost $88, and two
tables and three lamps cost $153, how much
does a lamp cost?
Answer:
One lamp is equal to 23 dollars
One table is equal to 42 dollars.
Step-by-step explanation:
We can solve this by first organizing what we have.
1 table (t) + 2 lamps (l) = 88.
2 tables (t) + 3 lamps (l) = 153.
_____________
===============
1t + 2l = 88
2t + 3l = 153
===============
-------------------------
If we multiply both sides by 2 on the first equation of
1t + 2l = 88
we could get
2t + 4l = 176.
If that is true, we can subtract the second equation of
2t + 3l = 153 from the new equation to get the price of a lamp.
2t + 4l = 176
- 2t + 3l = 153
____________
= 0t + l = 23
One lamp is equal to 23.
We can check this by plugging it into an equation.
1 + 2(23) = 88
1t + 46 = 88
1t + 46 - 46 = 88 - 46
1t = 42
If one table equals 42, we can put this back into the second equation to check.
2 (42) + 3 (23) = 153
84 + 69 = 153
That is correct.
Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.
Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.
Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.
Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.
2t + 3l = 153
- 1t + 2l = 88
____________
= t + l = 65
If t + l = 65, we can rearrange that equation to be something like t = 65 - l.
That means "t" is equal to 65 bucks minus a lamp.
We put this back into the first equation of
1t + 2l = 88
and replace "t" with the previous expression.
1(65 - l) + 2l = 88
Simplify/distributive property
65 - l + 2l = 88
65 - 65 - l + 2l = 88 - 65
-l + 2l = 23
l = 23
One lamp is equal to 23 bucks.
Confirmed :)
A lamp cost $23
Let the cost of a table be represented by x
Let the cost of a lamp be represented by y.
Since one table and two lamps cost $88, this can be represented as:
x + 2y = 88 ........ equation i
Since two tables and three lamps cost $153, this can be represented as:
2x + 3y = 153 ........ equation ii
Therefore, the equations are:
x + 2y = 88 ....... i
2x + 3y = 153 ....... ii
From equation i,
x + 2y = 88
x = 88 - 2y ...... iii
Put the value of x into equation ii
2x + 3y = 153
2(88 - 2y) + 3y = 153
176 - 4y + 3y = 153
Collect like terms
-4y + 3y = 153 - 176
-y = -23
y = 23
Therefore, a lamp cost $23
Read related question on:
https://brainly.com/question/15165519
Ivan is playing a skee-ball game. Different points are awarded depending on which hole the ball goes through. When the ball goes in the smallest hole, it is worth 100 points. When it goes in the bigger hole, it is worth 10 points, and when it does not go in either hole, it is worth 1 point. Ivan earned 352 points in the last game.
Which combination will result in a score greater than his current score?
2 balls in the smallest hole, and 8 balls in the bigger hole
4 balls in the smallest hole, and 6 balls in neither hole
3 balls in the smallest hole, 4 balls in the bigger hole, and 3 balls in neither hole
3 balls in the smallest hole, 3 balls in the bigger hole, and 4 balls in neither hole
Answer:
B.
Step-by-step explanation:
I don't know for a fact but i think its B. Sorry if I got it wrong.
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].
We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.
Now,
[tex]5500=229\times 24+4[/tex]
It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
[tex]5496+24=5520[/tex]
[tex]5520+24=5544[/tex]
[tex]5544+24=5568[/tex]
[tex]5568+24=5592[/tex]
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
PLEASE ANSWER QUICKLY Find the distance between points (4, 2) and (7, 2) on the coordinate
plane.
Answer:
3 units
Step-by-step explanation:
(4,2) (7,2)
Subtract 4 from 7 = 3
Subtract 2 from 2 = 0
This means that (7,2) is 3 units up from (4,2).
:) ur welcome
Answer:
Step-by-step explanation:
D=√(x2-x1)²+(y2-y1)²
D=√(7-4)²+(2-2)²
D=√(3)²+0
D=3²*½
D=3
Some number times 7 is equal to the number increased by 9
Write out the equation. Do not solve the equation.
Answer:
7x = x + 9.
Step-by-step explanation:
7 × something = something + 9, right?
So, 7x = x + 9.
Consignment Sale. Just Between Friends is the leading pop-up consignment sales event franchise in North America. The Des Moines event for Just Between Friends takes place each year at the Iowa State Fairgrounds for one week in the spring and one week in the fall. Families can earn money on gently used baby clothes, baby gear, maternity items, kids' clothes, shoes, toys, and books. Families sign-up as consignors and then price and tag their own items. At the end of the sale, consignors are given a check based on their item sales. Using historical records, the Des Moines event organizers advertise that their consignor check amounts follow a bell-shaped distribution (symmetric and unimodal) with a mean of $480 and a standard deviation of $110. Use the Empirical Rule: What percentage of consignors receive a check for more than $370
Answer:
Just Between Friends
The percentage of consignors who receive a check for more than $370 is:
= 16%.
Step-by-step explanation:
Mean of consignor check, μ = $480
Standard deviation, σ = $110
Value of check received, x > $370
Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:
z = (x-μ)/σ
z= ($370 - $480)/$110
z = -$110/$110
z = -1.00
Percentage of consignors who receive a check for more than $370
= 0.15866
= 0.16
= 16%
Diana adds either 2 or 5 to every whole number from 1 to 9. She wants to achieve as few different sums as
possible. What is the minimum number of different values she obtains?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
I need help solving this problem. Thanks
Answer:
Step-by-step explanation:
they say by noon 4 inches of rain has fallen, then the say that it's falling at 1/4 inch per hour
f(x) = 1/4x +4
where x is in hours, and f(x) represents the linear graph of the amount of rain that has fallen after noon :)
so by 2:30 or 2.5 hours.... then
f(2.5) = 1/4x +4
y = 1/4 (2.5) +4 ( i moved to the y b/c now there is an answer)
y =[tex]\frac{5}{8}[/tex] + 4
y =4[tex]\frac{5}{8}[/tex] inches of rain
Answer:
a) y = 1/4x + 4
b) 4.625 inches
Step-by-step explanation:
a) y(0) = 4 inches
slope = 1/4 rate
y = 1/4x + 4
b) 12:00pm (noon) to 2:30pm = 2 hours 30 mins = 2.5 hours
y = 1/4x + 4
y = (1/4)(2.5) + 4
y = 0.625 + 4
y = 4.625 inches
The equation for the pH of a substance is pH = -log[H], where Ht iS the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration
of hydrogen ions between the two solutions?
Answer:
The difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
Step-by-step explanation:
The pH is given by:
[tex] pH = -log[H^{+}] [/tex]
Where:
[tex] [H^{+}][/tex]: is the concentration of hydrogen ions.
For the basic solution (pH = 11.2), the concentration of H⁺ is given by:
[tex] [H^{+}]_{b} = 10^{-pH} = 10^{-11.2} = 6.31 \cdot 10^{-12} [/tex]
And, for the acidic solution (pH = 2.4) we have:
[tex] [H^{+}]_{a} = 10^{-pH} = 10^{-2.4} = 3.98 \cdot 10^{-3} [/tex]
Hence, the difference in the concentration of H⁺ between the two solutions is:
[tex] \Delta H^{+} = [H^{+}]_{a} - [H^{+}]_{b} = 3.98 \cdot 10^{-3} - 6.31\cdot 10^{-12} = 3.98 \cdot 10^{-3} [/tex]
Therefore, the difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
I hope it helps you!
Answer:
B. 4.0 x [tex]10^{-3}[/tex]
Step-by-step explanation:
EDG2021
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
The equation y - 5 = 6X + 1 is written as point-slope form. What is the equation written in slope intercept form
Answer:
y = 6x + 6
Step-by-step explanation:
The general formula is y = mx +cso; the y as seen will be constant as well as the x
With change of subject the 5 will be moved to the other side having y= 6x +1 + 5 .Given us y = 6x + 6.
Find the value of each expression:
1) 14 – 22
2) (10 + 5) – (32 – 3)
I need help pleaseeee
Find the product (-3/5) (-2/9)
Answer:
2/15
Step-by-step explanation:
(-3/5) (-2/9)
Rewriting
-3/9 * -2/5
-1/3 * -2/5
A negative times a negative is a positive.
2/15
whats the x and y value? I thought it would be choice d but I'm not sure
please help asap . my question is timed
Answer:
cos(60°) = [tex]\frac{adjacent}{hypotenuse}=\frac{y}{10\sqrt{3} }[/tex]
[tex]cos(60)=\frac{y}{10\sqrt{3} } \\y=cos(60) * 10\sqrt{3} \\y=\frac{1}{2} * 10\sqrt{3}\\y=\frac{10\sqrt{3}}{2} =5\frac{\sqrt{3} }{2} =8.66[/tex]
sin(60°) = [tex]\frac{opposite}{hypotenuse} =\frac{x}{10\sqrt{3} }[/tex]
[tex]sin(60)=\frac{x}{10\sqrt{3} } \\x=sin(60)*10\sqrt{3} \\x=\frac{\sqrt{3} }{2} *10\sqrt{3} \\x=\frac{10(\sqrt{3} ) (\sqrt{3} )}{2} \\x=\frac{10*3}{2} =\frac{30}{2} =15[/tex]
