Hey there!
When dealing with percent word problems, the word "is" means equals. Let's see what we can do with your problem.
If the small school had 60% boys, it will have 40% girls. The number of boys is 48, which should equal 60% of the total, which we can model below, with t representing the total number of kids. In decimal form, 60% is 0.6.
0.6t=48
We divide both sides by 0.6.
t=80
Therefore, there are 80 total kids at the school.
We can also check our answer below.
BOYS: 0.6(80)= 48
GIRLS: 0.4(80)=32
48+32=80
I hope that this helps!
p(x) is a polynomial p(x) divided by (x-9) has a remainder of 1. P(x) divided by (x-4) has a remainder of 7. P(x) divided by (x+4) has a remainder of 0. P(x) divided by (x+9) has a remainder of -5
P(4)=?
P(-9)=?
Answer:
[tex]P(4)=7\,,\,P(-9)=-5[/tex]
Step-by-step explanation:
Given: P(x) has a remainder 1 when divided by [tex]x-9[/tex], P(x) has a remainder 7 when divided by [tex]x-4[/tex], P(x) has a remainder 0 when divided by [tex]x+4[/tex] and P(x) has a remainder -5 when divided by [tex]x+9[/tex]
To find: [tex]P(4),P(-9)[/tex]
Solution:
According to remainder theorem, when a polynomial [tex]P(x)[/tex] is divided by a polynomial [tex]x-a[/tex], the remainder obtained is equal to [tex]P(a)[/tex].
As P(x) has a remainder 7 when divided by [tex]x-4[/tex],
[tex]P(4)=7[/tex]
As P(x) has a remainder -5 when divided by [tex]x+9[/tex],
[tex]P(-9)=-5[/tex]
Which statement is an example of the transitive property of congruence?
O A. If AKLME APQR, then APQR=ASTU.
O B. If AKLME APQR and APOR=ASTU, then AKLME ASTU.
C. AKLM: AKLM.
O D. If AKLME APOR, then APORE AKLM.
Answer:
B. If ΔKLM ≅ ΔPQR and ΔPQR ≅ ΔSTU, then ΔKLM ≅ ΔSTU
Step-by-step explanation:
The transitive property in general says ...
if a=b and b=c, then a=c
The transitive property of congruence replaces the equal sign with a congruence symbol, and replaces a, b, c with any geometric figure. Here, the geometric figures used are triangles KLM, PQR, and STU.
If ΔKLM ≅ ΔPQR and ΔPQR ≅ ΔSTU, then ΔKLM ≅ ΔSTU
hus, D satisfying (ABC)DequalsI exists. Why does the expression for D found above also satisfy D(ABC)equalsI, thereby showing that ABC is invertible? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. After substituting the expression for D, the product DABC simplifies to I by repeated application of the associative property and the definition of inverse matrices. B. After substituting the expression for D, left multiplying the product by nothing results in the equation IequalsABCD. C. After substituting the expression for D, taking the inverse of both sides of the equation results in the equation IequalsABCD. D. After substituting the expression for D, right multiplying the pr
Complete Question
The complete question is shown on the first uploaded image
Answer:
First Question
Option A is correct
Second Question
Option C is correct
Third Question
[tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]
Fourth Question
So substituting for D in (ABC) D = I
[tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]
[tex]I = I[/tex]
This proof that ABC is invertible
Step-by-step explanation:
From the question we are told that
A , B and C are invertible which means that [tex]A^{-1} , B^{-1}, C^{-1}[/tex] exist
Now
From the question
(ABC) D = I
Where I is an identity matrix
Now when we multiply both sides by [tex]A^{-1}[/tex] we have
[tex]A^{-1} A BCD = A^{-1} * I[/tex]
[tex]IBCD = A^{-1}[/tex]
Now when we multiply both sides by [tex]B^{-1}[/tex] we have
[tex]B^{-1 } *I BCD = A^{-1} * B^{-1}[/tex]
[tex]I CD = A^{-1} * B^{-1}[/tex]
Now when we multiply both sides by [tex]C^{-1}[/tex] we have
[tex]C^{-1} * I CD = A^{-1} * B^{-1} * C^{-1}[/tex]
[tex]I D = A^{-1} * B^{-1} * C^{-1}[/tex]
[tex]D = A^{-1} * B^{-1} * C^{-1}[/tex]
So substituting for D in the above equation
[tex](ABC) * A^{-1} * B^{-1} * C^{-1} = I[/tex]
[tex]I = I[/tex]
This proof that ABC is invertible
You are given the five number summary from a set of data as follows: Minimum=5, Q1=7, Median=8, Q3=11.5 and Maximum=15. Explain how to find the difference between the Range and the Interquartile Range. Find this difference.
Answer:
a) Range =10
b) inter quartile range = 4.5
Step-by-step explanation:
Explanation:-
Given minimum =5
Median=8
upper quartile (Q3) =11.5
Lower quartile range= 7
Maximum=15
a) Range = maximum value -minimum value
= 15 -5
= 10
b) Interquartile Range = median of upper half - median of lower half
= Q₃- Q₁
= 11.5 - 7
= 4.5
Given y = 4x + 3, what effect does changing the equation to y = 4x - 3 have on the y-intercept?
A)
graph becomes steeper
B)
no change to y-intercept
C)
graph moves down 3 units
D)
graph moves down 6 units
Answer:
graph moves down 6 units
Step-by-step explanation:
Y intercept of a line is point on y axis where the line crosses the y-axis.
Since the line is of the slope intercept form y = mx+ c
where m is slope of line and c is y intercept
_________________________________________________
Equation of old line : y = 4x + 3
then for equation y = 4x + 3
m: 4 and c = 3
Thus y intercept is +3 unit above the X axis
_________________________________________________
Equation of new line : y = 4x - 3
Similarly based on above explanation
m: 4 and c = -3
Thus y intercept is +3 unit below the X axis.
Thus we can see that y intercept has moved downward
Lets calculate no. of units it moved downward
Distance between them is 3 - (-3) = 6 unit
Thus graph moved 6 units downwards.
Steepness of graph depends on slope of line. The slope is 4 for both the lines and hence there is no change in steepness.
Thus correct answer is graph moves down 6 units
What is the volume of the cone in the diagram
A. 150 pi cubic units
B. 200 pi cubic units
C. 250 pi cubic units
D. 300 pi cubic units
Answer:
A
150 pi cubic units
Step-by-step explanation:
Answer:
Substituting the values r = 5 and h = 18 in the formula V=1/3×πr^2h, you get V=1/3×π×52×18 = 150π cubic units.
Step-by-step explanation:
write the linear function if f(0)=5 and f(2)=35
Answer: y=15x+5
Step-by-step explanation:
Looking at what we are given, we can tell that the y-intercept is 5. To ge tthe slope, you use [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]. With the slope , you get 15.
A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation 14 pounds.
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean weight loss yield of the powder diet and μ2 be the mean weight loss yield of the liquid diet.
The random variable is μ1 - μ2 = difference in the mean weight loss yield of the powder diet and the mean weight loss yield of the liquid diet.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This us a left tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(μ1 - μ2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 42
μ2 = 45
s1 = 12
s2 = 14
n1 = 49
n2 = 36
t = (42 - 45)/√(12²/49 + 14²/36)
t = - 1.04
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [12²/49 + 14²/36]²/[(1/49 - 1)(12²/49)² + (1/36 - 1)(14²/36)²] = 70.28/1.03
df = 68
We would determine the probability value from the t test calculator. It becomes
p value = 0.15
Assuming a significance level of 0.05, then
Since alpha, 0.05 < than the p value, 0.15, then we would fail to reject the null hypothesis. Therefore, we can conclude that at a 5% significance level, the liquid diet does not yield a higher mean weight loss than the powder diet.
Just give me the answer no expiation.
Answer:
b. 424
Step-by-step explanation:
it gives the equation N=41b+137
N=41(7)+137
N=424
A right rectangular prism has a height of 15 meters, a length of 4 meters, and a width of 3 meters. Which expressions show how
to calculate the volume? Check all that apply.
VX
2(15+4+3)
15 +4+3
3(4) + 15
60(3)
12(15)
15(4(3)
2(4)(3)(15)
60(4)
Answer:
60(3), 12(15), 15(3)(4)
Step-by-step explanation:
volume of a rectangular prism is the product of all sides which is 15*3*4. 60(3), 12(15), 15(3)(4) are the only ones equal to that.
Answer:
D,E,F
Step-by-step explanation:
bo and Luke are driving to uncle Jesse's house their car at the generally can go nearly 208 miles on 13 gallons of gas they only have 3 gallons of gas left in the tank but they are 42 miles away from uncle Jesse's house how far can the generally go on 3 gallons of gas in its tank
Answer:
48 miles
Step-by-step explanation:
What we must do is calculate the car's performance, that is, the number of miles per gallon of gas, like this:
208/13 = 16
which means that for each gallon of gas you can travel a total of 16 miles.
They tell us they have 3 gallons of gasoline left so they can go:
16 * 3 = 48
If your goal is 42 miles away, that means you can make it and you still have 6 more miles to go.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
5x - 1
Step-by-step explanation:
f(x) = 3x - 2
g(x) = 2x + 1
(3x - 2) + (2x + 1)
3x + 2x = 5x
-2 + 1 = -1
Answer: 5x - 1
The number of new cars (c) a ship carries can’t exceed 975
Answer:
That may or may not be true, depending one the ship size.
Step-by-step explanation:
'Can't really give a proper answer, to somethings that's not a q. *shrug*
A man travelled 450 km on the first day and 565,000 m on the second and the third day he travel double the distance you travel on the first day on the fourth day he reached his destination which was 2500km from his starting point how far did he travel on the fourth
Answer:
1000miles
Step-by-step explanation:
A men travel 585 km on fourth day.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
A man travelled 450 km on the first day and 565,000 m on the second day, the third day he travel double the distance you travel on the first day.
Here, On the fourth day he reached his destination which was 2500km from his starting point.
Let the distance he travel on the fourth day = x
So, We can formulate;
⇒ 450 km + 565,000 m + 2 × 450 km + x = 2500 km
⇒ 450 km + 565 km + 900 km + x = 2500 km
⇒ 1915 km + x = 2500 km
⇒ x = 2500 - 1915
⇒ x = 585 km
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What is the quotient when the sum of 13 and 11 is divided by the difference of 13 and 11
Answer:
12
Step-by-step explanation:
[tex]\dfrac{13+11}{13-11}=\dfrac{24}{2}=12[/tex]
Hope this helps!
On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, he will hear five random digits on the next trial. The participant's score is the longest string of digits he can successfully repeat.
A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.63 digits.
a. The expected value of the mean of the 49 randomly selected students, M, is:_____
b. The standard error of M is:______
Answer:
a) The expected value of the mean of the 49 randomly selected students, M, is 7.06 digits
b)
The Standard error of the mean is 0.2328
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 49
The Expected value of the mean of 49 randomly selected students
μₓ = μ =7.06 digits
b)
The Standard error of the mean determined by
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Given sample size 'n' = 49
The Standard deviation 'σ' = 1.63 digits
The Standard error
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
[tex]S.E = \frac{1.63}{\sqrt{49} } = 0.2328[/tex]
Final answer:-
a) The expected value of the mean of the 49 randomly selected students, M, is 7.06 digits
b) The Standard error of the mean is 0.2328
A cone-shaped pile of sawdust has a base diameter of 36 feet, and is 14 feet tall. Find the volume of the pile.
The volume of the cone-shaped pile of sawdust is, 4752 cubic feet.
What is cone?A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
Given that,
Diameter of cone 2r = 36 feet,
Height of cone h = 14 feet.
Since, diameter 2r = 36 ⇒ r = 18 feet
The volume of the cone V = 1/3×π×r²×h
V = 1/3×22/7×18×18×14
= 4752 cubic feet
The volume of the cone-shaped pile is, 4752 cubic feet.
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solve for 4/5 x ( -2/9 )
Answer:
-8/45
Step-by-step explanation:
4/5 * -2/9
Multiply the numerators
4*-2 = -8
Multiply the denominators
5*9 = 45
numerator over denominator
-8/45
a green and a red die are tossed. what is the probability that a 4 shows
on the green die and a 5 shows on the red die.
Answer:
1/36
Step-by-step explanation:
The probability of getting green is 1/6
and the probability of getting red is 1/6.
Now,we want to know the probability of getting red and green. In probability,the word 'and' means times.
So it would be;
1/6 times 1/6
= 1/36
Florida reappraises real estate every year, so the county appraiser's Web site lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. Here are the appraised market values and actual selling prices (in thousands of dollars) of condominium units sold in a beachfront building in a 93-month period:
Selling price 832 878 628 1067 924 792 645 854
Appraisal value 744.7 842.8 480.9 1005.2 787.9 758.3 548.9 634.3
Selling price 764 708 752 862 720 1099 1301 800
Appraisal value 641.7 514.8 552.9 747.4 475.5 756.3 1039.4 582.8
Here is part of the Minitab output for regressing selling price on appraised value:
Predictor Coef SE Coef T
Constant 227.0989 95.044 2.389
Appraisal 0.8991 0.133 6.76
S = 88.7959 R-Sq = 76.5% R-Sq (adj) = 74.9%
The equation of the least square regression line for predicting selling price from appraised value is (round your answer to at least four decimals):
price appraised value.
Answer:
The equation of the least square regression line for predicting selling price from appraised value is:
[tex]\text{Selling Price}=227.0989 + 0.8991\ \text{Appraised Value}[/tex]
Step-by-step explanation:
The general form of the least square regression line is:
[tex]y=a+bx[/tex]
Here,
y = dependent variable
x = independent variable
a = y-intercept
b = slope
The Minitab output for regressing selling price on appraised value is:
Predictor Coef SE Coef T
Constant 227.0989 95.044 2.389
Appraisal 0.8991 0.133 6.76
S = 88.7959
R-Sq = 76.5%
R-Sq (adj) = 74.9%
The constant term in the regression output represents the y-intercept and the Appraisal coefficient the slope of the regression line.
Then the equation of the least square regression line for predicting selling price from appraised value is:
[tex]\text{Selling Price}=227.0989 + 0.8991\ \text{Appraised Value}[/tex]
ASAP PLEASE
Mike and Jhon has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Mike uses the formula V = π(3)2(7) to find the volume whereas Jhon says his formula V= V = 1/3π(3)2(7) is correct to find the volume.
Who is incorrect ? and why?
Answer:
I can't really see the whole question, but for a cone the volume formula is πr2h
3
Step-by-step explanation:
A large pizza costs $8.95, plus $0.65 for each additional topping. Ron paid $10.90 for a large pizza. How many additional toppings did he get?
(please show all your work with a let, so, equation(and solution) and therefore statement).
What is the surface area of the rectangular pyramid? m2 18 point for how ever awncers this first
Answer:
When all side faces are same
surface area = lw + 1/2 × perimeter × slant height.
When the side faces are different
surface area = base area + lateral area
Step-by-step explanation:
The question you ask is the formula one can use to calculate the surface area of a rectangular pyramid.
The base of a rectangular pyramid is rectangular. The picture below shows how a rectangular pyramid looks like .
The surface area of the rectangular pyramid includes the area of the base and areas of all the triangular faces. This simply implies the area of the rectangular base and the area of each triangular faces. Mathematically, it can be represented below.
The base area(rectangle) = length × width = lw
Area of a triangle = 1/2 × base × height = 1/2bh
Therefore, if all the faces of the triangle are the same(regular pyramid) the total surface area will be
surface area = lw + 1/2 × perimeter × slant height.
Note the triangular faces are 4 in numbers.
If all the sides of the triangle are different the surface are will be
surface area = base area + lateral area
We have to add the triangular faces individually for an irregular pyramid.
Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the numerous types of solder defects (e.g., pad non-wetting, knee visibility, voids) and even the degree to which a joint possesses one or more of these defects. Consequently, even highly trained inspectors can disagree on the disposition of a particular joint. In one batch of 10,000 joints, inspector A found742that were judged defective, inspector B found745such joints, and1145of the joints were judged defective by at least one of the inspectors. Suppose that one of the 10,000 joints is randomly selected.
(a) What is the probability that the selected joint was judged to be defective by neither of the two inspectors? (Enter your answer to four decimal places.)
(b) What is the probability that the selected joint was judged to be defective by inspector B but not by inspector A? (Enter your answer to four decimal places.)
Answer:
a
The probability that the selected joint was judged to be defective by neither of the two inspectors is [tex]P(A' n B' ) = 0.8855[/tex]
b
The probability that the selected joint was judged to be defective by inspector B but not by inspector A is [tex]P(A' n B) =0.0403[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_s = 10000[/tex]
The number of outcome for inspector A is [tex]n__{A}} = 742[/tex]
The number of outcome for inspector B is [tex]n__{B}} = 745[/tex]
The number of joints judged defective by both inspector is [tex]n(A u B) = 1145[/tex]
The the probability that the selected joint was judged to be defective by neither of the two inspectors is mathematically represented as
[tex]P(A' n B' ) = 1 - P(A u B)[/tex]
Now
[tex]P(A\ u \ B) = \frac{n(Au B)}{n_s }[/tex]
substituting values
[tex]P(A\ u \ B) = \frac{1145}{ 10 000 }[/tex]
So
[tex]P(A' n B' ) = 1 - \frac{1145}{10 000}[/tex]
[tex]P(A' n B' ) = 0.8855[/tex]
the probability that the selected joint was judged to be defective by inspector B but not by inspector A is mathematically represented as
[tex]P(A' n B) = P(A \ u \ B) -P(A)[/tex]
Now
[tex]P(A) = \frac{n__{A}}{n_s}[/tex]
substituting values
[tex]P(A) = \frac{742}{10 000}[/tex]
So
[tex]P(A' n B) = \frac{1145}{10 000} - \frac{742}{10 000}[/tex]
[tex]P(A' n B) =0.0403[/tex]
15 cm
12 cm
7 cm find area
Answer:
1260cm^2
Step-by-step explanation:
15 times 12 = 180
180 times 7 = 1260
If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph?
04
08
O 12
0 16
what does 1/2 (40x60) =
What is the equivalent equation solved for h?
Answer:
[tex]h=\frac{P}{mg}[/tex]
Step-by-step explanation:
If you divide both sides of this equation by mg, you are left with [tex]h=\frac{P}{mg}[/tex], which is the equivalent solution solved for h. Hope this helps!
Answer:
it's B
Step-by-step explanation:
Natalia is moving into a new house. All together, her furniture weighs 3,204 pounds. If it takes 8 trucks to carry all of Natalia's furniture, what is the average weight load on each truck? A. 640.8 pounds per truck B. 801 pounds per truck C. 1,602 pounds per truck D. 400.5 pounds per truck
Answer:
D
Step-by-step explanation:
The average can be found by dividing the number of pieces (or trucks in this case) by the total, so 3204/8=400.5 pounds, or D as our answer
What is the measure of the whole angle?
Answer:
130
Step-by-step explanation:
60° + 70° = x
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we took away 60 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.
60 + 70 = x
→ Simplify
130 = x
x = 130°