Answer:
30.7
Step-by-step explanation:
sin 71° = 29/ ladder length
so length = 29/ sin 71° = 30.7
Find the length of the midsegment of trapezoid ABCD.
pls show yr work
Answer:26
Step-by-step explanation: Base one plus Base 2 divided by 2
A certain amount of money is shared between Harvey and Mike in the ratio 4:3. If Mike gets £ 75 less than Harvey, find the total amount of money.(will mark brainliest)
Based on their sharing ratio of 4:3, when Mike gets £ 75 less than Harvey, the total amount of money shared is $525.
How is the total amount determined?The total amount being shared between Harvey and Mike is determined using the arithmetic of ratios.
Firstly, we determine the sum of ratios as 7. Since Mike's share is 3/7, which is less by £75 than Harvey's share, which is 4/7, we find the difference as 1/7 and equate it to £75.
Proportionately, if 1/7 equals £75, the total sum being shared will be equal to $525 (£75 x 7/1)
Sharing ratio between Harvey and Mike = 4:3
Sum of ratios = 7
Let the amount Harvey gets = x
x = 4/7
Let the amount Mike gets = x - 75
x - 75 = 3/7
4/7 - 3/7 = 1/7
1/7 = £75
7 = £525 (£75 x 7/1)
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the volume of a cone varies jointly with the base (area) and the height. the volume is 12.5 ft 3 when the base (area) is 15 ft 2 and the height is 2 1 2 ft . find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft 2 and the height is 6 ft . 112.5 ft 3 18.75 ft 3 72 ft 3 24 ft 3
The volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.
Let the constant of variation be k. We know that the volume of a cone is given by the formula:
V = (1/3)πr²h
where r is the radius of the base and h is the height. Since the base area is given by πr², we can write:
V = (1/3)Bh
where B is the base area. From the given information, we know that:
12.5 = (1/3) * 15 * (2(1)/(2))
Solving for k, we get:
k = 12.5 / (15 * (2(1)/(2))) = (12.5 * 2) / 15 = 5/3
Now that we have found the variation constant, we can use it to find the volume when the base area is 12ft² and the height is 6ft:
V = (5/3) * 12 * 6 = 60 ft³
So the volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.
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In a group of 40 pupils, 15 play the flute only. 7 play the piano only. 5 play both instruments. A student is chosen at random. What is the probability the student plays neither instrument?
Answer:
13/40
Step-by-step explanation:
Total No of pupils = 40
No of pupils who play the flute = 15
No of pupils who play the Piano = 7
No of pupils who play both = 5
Total No of pupils who can play the atleast one instrument = 15+5+7= 27
No one pupils who play neither instrument = 40 - 27 = 13
Probability of a pupil being chosen at random who plays neither instrument = No of Pupils who play neither instrument/ Total No of pupils = 13/40
Therefore the answer will be 13/40
A system of linear equations is graphed below.
Which coordinate point represents the solution?
(2, 2)
(0, 40)
(40, 0)
(20, 20)
Answer:
it could be 20 and 20 or 0 and 40
Dean is helping his mom make a fence for their rectangular vegetable garden. First, they measure the sides and find that it is 20 feet long and 40 feet wide. Then, they buy fencing from the hardware store. If the store sells fencing in 4-yard packages, how many packages do Dean and his mom need?
Answer:
10 packages
Step-by-step explanation:
To find the number of 4 yard packages for the fencing, we need to find the perimeter of the fence.
Perimeter = 2*(20 + 40)
Perimeter = 2*60 = 120 feet
*It is important to note that the perimeter is in feet and the packages are in yards*
4 yards = 12 feet
120 / 12 = 10 packages
Recent Review
1. Write an equation in standard form of a line that has a slope of 4 and passes through the point (-4,-4).
An equation in standard form of a line that has a slope of 4 and passes through the point (-4, -4) is y = 4x + 12.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-4, -4), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-4) = 4(x - (-4))
y + 4 = 4(x + 4)
y + 4 = 4x + 16
y = 4x + 16 - 4
y = 4x + 12
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suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.52 . using the empirical rule, what percentage of american women have shoe sizes that are between 3.48 and 12.6 ?
The percentage of American women with shoe sizes between 3.48 and 12.6 is somewhere between 68% and 95%.
Empirical Rule Shoe SizesThe empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.
In this case, we want to find the percentage of American women with shoe sizes between 3.48 and 12.6. To use the empirical rule, we need to convert these values to standard deviations away from the mean. We can do this by subtracting the mean and dividing by the standard deviation:
3.48 - 8.04 = -4.56
-4.56 / 1.52 = -3.00
12.6 - 8.04 = 4.56
4.56 / 1.52 = 2.99
So we want to find the percentage of American women with shoe sizes that are between -3 standard deviations and +2.99 standard deviations from the mean.
According to the empirical rule, about 68% of the data falls within one standard deviation of the mean, so we can estimate that about 68% of the data falls within -1 and +1 standard deviations from the mean. The percentage between -2 and +2 standard deviations from the mean would be about 95%, and between -3 and +3 standard deviations from the mean would be about 99.7%.
Since our range of shoe sizes is partially contained within each of these ranges, we can estimate that the percentage of American women with shoe sizes between 3.48 and 12.6 is somewhere between 68% and 95%.
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Can y’all help me out please,
Answer:
I don't know the answer.
Step-by-step explanation:
Sorry. ;(
←
Use inductive reasoning to predict the next line in the sequence of computations. Then use a calculator or perform the
arithmetic by hand to determine whether your conjecture is correct.
11x9,091 100,001
22x9,091 = 200,002
33x9,091 = 300,003
44 x 9,091 400,004
Answer:
55 x 9091 = 500,005
Step-by-step explanation:
This checks with a calculator
Camp cool algebra question number 1.
How many children will be in the camp in 3 years?
Answer:8750
Step-by-step explanation:
I did 5000 times .25(1/4 as a decimal) which equals 1250. Then 1250 times 3(year) equals 3750. 5000 plus 3750 is 8750
A coordinate grid with one line labeled 3 y equals 2 x minus 9. The line passes through points at (0, negative 3) and (3, negative 1).
Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x – 9. Which could be the other equation?
The system of equations will be:-
6y=4x-18
9y=6x-27
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
For a system to have an infinite number of solutions, the slopes and y-intercepts of the slope must be the same.
We have that one of the equations of the system is 3y = 2x – 9.
We generate another equation that has the same slope and y-intercept by just multiplying through by a non-zero constant.
Let us multiply by 2.
2(3y = 2x – 9)---->6y=4x-18
Or multiply through by 4 to get:
3(3y = 2x – 9)----->9y=6x-27
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Joe went to a taco stand with some friends. Joe bought 9 tacos and 4 burritos, and spent 64% of the money on burritos. How many tacos could Joe but for the price of one burrito?
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Joe can have four tacos for the cost of one burrito.
The cost of 4 burritos is 64%, which means the cost of 1 burrito is 16%.
The cost of 9 tacos is 36%, which means the cost of 1 taco is 4%.
1 taco Is 4%, 1 burrito = 16%
4 times 4 equals 16
Joe can get four tacos for the price of one burrito.
(Hope this helps!)
(Consider marking as the brainliest, so I can get to the next rank please :)
What is; 24x - 5 - 3
Answer:
Step-by-step explanation:
24x - 5 - 3 can be simplified by combining the constants (-5 and -3) into a single constant (-8):
24x - 5 - 3 = 24x - 8
Therefore, the simplified expression is 24x - 8.
Answer: 24x - 2
Step-by-step explanation:
You can't subtract the Coefficient and the Natural Number, so you can only do 24x - (5 - 3)
Which will end up as 24x - 2.
need help with b and c
a. The real annual interest rate is 1.6%
b. He made $14871 after 25 years in account.
What is the interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Here, we have
Given: A taxpayer who pays 22% in taxes each year has these two accounts. Account 1: $10000 is placed in a tax-deferred account that pays 2.1% interest compounded annually for 25 years. Account 2: $10000 is placed in a taxable account that pays 3.1% interest compounded annually for 25 years.
b. His real annual interest rate is the interest rate decreased by the product of the interest rate and the tax rate.
Actual annual interest rate = 2.1% - (22% × 2.1%)
= 1.6%
Hence, the real annual interest rate is 1.6%
c. P = $10000 , n= 25, r = 1.6%
Compound interest = p(1+(r/100))ⁿ
= 10000(1+(1.6/100))²⁵
= $14871
Hence, he made $14871 after 25 years in account.
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After collecting more data, Mai reports that the proportion of students who think it's a good idea to change school hours is 90% with a margin of error of 3%. What does this mean?
Answer:
See below
Step-by-step explanation:
What is margin of error?
Since it is impossible to predict results of a statistical survey on a sample population with 100% accuracy, scientists often include an error in estimation along with the calculated proportion
This margin of error tells you how many percentage points your results will differ from the real population value
Here the estimated proportion is 90%Margin of error is 3%So actual population proportion will be 90% ± 3%90 - 3 = 87, 90 + 3 = 93So actual proportion will lie between 87% and 90% ANSWERFind the distance between X(−3,−2) and Y(−6,5)
The distance between the points (-3, -2) and (-6, 5) is 7.62 units.
How to find the distance between the two points?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √( (x₁ - x₂)² + (y₂ - y₁)²)
So here, the distance between (-3, -2) and (-6, 5) will be:
d = √( (-3 + 6)² + (-2 - 5)²)
d = √( 58) = 7.62
The distance between the points X(−3,−2) and Y(−6,5) is 7.62 units.
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A grocer has two kinds of nuts. One costs $5 kg and the other costs $4.20 kg . How many kg of each type of nut should be mixed in order to get 60 kg of a mixture worth $4.80kg
45 kg of one nut and 45 kg of another nut should be mixed in order to get 60 kg of a mixture worth $4.80kg.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
One nut = x kg
Cost = $5
Other nuts = y kg
Cost = $4.20
Now,
From the given statement we can make two equations.
x + y = 60
x = 60 - y
Substituting here,
5x + 4.20y = 4.80
5 (60 - y) + 4.20y = 4.80 x 60
300 - 5y + 4.20y = 288
300 - 288 = 5y - 4.20y
12 = 0.8y
y = 12/0.8
y = 15
Now,
x = 60 - 15
x = 45
Thus,
45 kg of one nut and 45 kg of another nut.
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At still Bay Middle School, 3 out of 5 teachers have earned their masters degrees. If there are 30 teachers at the school, how many of them have earned their masters degrees?
Based on the given ratio, the number of teachers at Still Bay Middle School, who have earned their master's degrees, is 18.
What is the ratio?The ratio is the relative size of a value compared to another.
Ratios are depicted as percentages, fractions, or decimals, to show that they are fractional values, representing a portion of a whole.
The ratio of teachers who have earned their master's = 3/5
The total number of teachers at the school = 30
The number of teachers with masters = 18 (30 x 3/5)
The number of teachers without masters = 2/5 (1 - 3/5)
= 12 (30 x 2/5)
Thus, since 3 out of 5 teachers at Still Bay Middle School have earned their master's degrees, the number is 18 if there are 30 teachers at the school.
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A factory produces 900 items per week at a unit cost of $75 new equipment is installed that increases the productivity by 12% and reduces the unit cost by 16%
a) The new production rate is 1008 items per week.
b) The new unit cost is $63.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
a) The new production rate can be calculated by increasing the old production rate of 900 items per week by 12%.
New production rate = 900 items/week + 12% of 900 items/week
New production rate = 900 items/week + (12/100) x 900 items/week
New production rate = 900 items/week + 108 items/week
New production rate = 1008 items/week
So, the new production rate is 1008 items per week.
b) The new unit cost can be calculated by reducing the old unit cost of $75 by 16%.
New unit cost = $75 - 16% of $75
New unit cost = $75 - (16/100) x $75
New unit cost = $75 - $12
New unit cost = $63
So, the new unit cost is $63.
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The question seems incomplete, the missing part has been below:
A factory produces 900 items per week at a unit cost of $75 new equipment is installed that increases productivity by 12% and reduces the unit cost by 16%.
a) What is the new production rate?
b) What is the new unit cost?
Express cos a in terms of sin a
Answer:
Step-by-step explanation:
We know that
[tex]sin^2a+cos^2a = 1[/tex],
so if we rearrange that and solve for [tex]cosa[/tex] then we get
[tex]cosa[/tex] = ± [tex]\sqrt{1-sin^2a}[/tex]
i need help with this assignment
The mean of the scores is given as follows:
88.3.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Considering the absolute frequencies in the table, the sum of all the observations is given as follows:
1 x 75 + 9 x 80 + 3 x 85 + 2 x 90 + 2 x 95 + 7 x 100 = 2120.
The number of students is given as follows:
1 + 9 + 3 + 2 + 2 + 7 = 24.
Hence the mean is obtained as follows:
2120/24 = 88.3.
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Pleaseee HELP ASAP PLEASE
The triangles are not similar.
How to find similar triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles congruent to each other.
Therefore, for the triangles above to be similar the angles will be congruent and the sides will be a ratio of each other.
Therefore, the similarities statement for the two triangle can be represented as follows:
The triangles are not similar because the sides are not a ratio of each other.
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Find the value of x
(17x + 14)°
(4x - 2)°
Answer:
x= 8
Step-by-step explanation:
17x+14+4x-2= 180
21x= 168
x= 8
£200 is invested for 10 years at 9 compound interest per annum
After 10 years, the investment of £200 at 9% compound interest per annum would be worth approximately £432.97.
The amount of money that would be obtained after 10 years can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = initial principal (£200)
r = interest rate (9%)
n = number of times compounded per year
t = number of years invested (10)
For an interest rate compounded annually, n = 1. Plugging in the values into the formula, we have:
A = £200 * (1 + 0.09/1)^(1 * 10)
A = £200 * (1.09)^10
A = £200 * 2.1669
A = £433.38
Therefore, £433.38 would be obtained after 10 years of investing £200 at 9% compound interest per annum.
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simplify the following:
-3/4/-6 (the / are for fractions)
Answer:
[tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
[tex]\frac{-3/4}{6}=\frac{-0.75}{6}[/tex]
[tex]\frac{6}{-0.75}=-8[/tex]
[tex]\frac{-0.75}{6}=\frac{-1}{8}[/tex]
Yosemite Falls, the highest waterfall in the United States, is actually made up of three smaller falls. The Lower Yosemite Falls is 355 feet shorter than the Middle Cascades Falls. The Upper Yosemite Falls is 80 feet more than twice the Middle Cascades Falls. If the entire set of waterfalls is 2425 feet long, how tall is Lower Yosemite Falls?
As per unitary method Lower Yosemite Falls is 292.5 feet tall.
The unitary method is a mathematical problem-solving technique that involves using known information to find unknown information.
Let x be the height of the Middle Cascades Falls. The height of the Lower Yosemite Falls is 355 feet shorter than x, so the equation is:
Lower Yosemite Falls = x - 355
The height of the Upper Yosemite Falls is 80 feet more than twice the height of the Middle Cascades Falls, so the equation is:
Upper Yosemite Falls = 2x + 80
The total height of all three falls is 2425 feet, so we can add the heights of each fall to find the equation:
Lower Yosemite Falls + Middle Cascades Falls + Upper Yosemite Falls = 2425
Substituting in our previous equations:
x - 355 + x + 2x + 80 = 2425
Simplifying:
4x = 2425 + 355 - 80
4x = 2590
Dividing both sides by 4:
x = 647.5
So, the height of the Middle Cascades Falls is 647.5 feet. To find the height of the Lower Yosemite Falls, we substitute x back into the first equation:
Lower Yosemite Falls = x - 355
Lower Yosemite Falls = 647.5 - 355
Lower Yosemite Falls = 292.5 feet
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At which point would the graphs of the equations below intersect?
(-2,-1)
(2,-1)
(-1,2)
(-1,-2)
The point at which the graphs of the equations would intersect is given as follows:
(-2, -1).
Which is the point that the two functions would intersect?The point at which the two functions would intersect is the solution to the system of equations in this problem.
The equations are given as follows:
3x - 4y = -2.-6x + 5y = 7.Multiplying the first equation by 2, we have that:
6x - 8y = -4.-6x + 5y = 7.Adding the two equations, the solution for y is obtained as follows:
-3y = 3
3y = -3
y = -1.
Hence the solution for x is obtained as follows:
3x - 4(-1) = -2
3x + 4 = -2
3x = -6
x = -2.
Hence the point is:
(-2, -1).
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Evaluate the expression for the given value of the variables.
0.7d - 2.1f=
d= 15, f= 3
0.7d - 2.1f = Answer?
Answer:
16.8
Step-by-step explanation:
First, plug in the values given.
(0.7*15) - (2.1*3)
From there, it's simple math. Multiply what is in the parentheses first,
10.5 + 6.3
then add together the sums
16.8.
Use the two-way frequency table to complete the relative frequency table. Drag the numbers into the boxes.
Lunch Order
Sandwich Pasta
Total
19
15
34
Sport
Volleyball
Swimming
Total
26
10
36
45
25
70
14
21
27
36
37
49
51
64
100
Lunch Order
Sandwich
Pasta
Total
Volleyball
%
%
%
Sport Swimming
%
%
%
Total
%
%
%
By applying the relative frequency concept, we make this table to represent the relative frequency of the problem:
Lunch order
Sandwich Pasta Total
Volleyball 27% 21% 49%
Swimming 37% 14% 51%
Total 64% 36% 100%
Relative frequency is a percentage number that states the amount of data in a certain group.
Relative frequency is given by the number of desired outcomes, also called frequency, divided by the number of total outcomes.
We already have the following information:
Lunch order
Sandwich Pasta Total
Volleyball 19 15 34
Swimming 26 10 36
Total 45 25 70
Now we want to find the relative frequency and put it into the following table:
Lunch order
Sandwich Pasta Total
Volleyball 19/70*100% = 27% 15/70*100% = 21% 34/70*100% = 49%
Swimming 26/70*100% = 37% 10/70*100% = 14% 36/70*100% = 51%
Total 45/70*100% = 64% 25/70*100% = 36% 70/70*100% = 100%
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