Answer:
nine hundred five thousand two hundred thirty-eight
An after-school care facility tries to maintain a 2-to-1 ratio of children to adults. If the facility hired five adults, what is the maximum number of children that can enroll?
Answer:
10 children
Step-by-step explanation:
If we have a ratio of 2:1 children:adults, then we can find out how many children max can enroll if there are 5 adults.
Our original ratio was 2:1 and now it's x:5, assuming x is the number of children enrolled. We multiply 1 by 5 to get to 5, so we need to multiply 2 by 5 to get the total number of chlidren.
2 × 5 = 10
Hope this helped!
#if a sum become rs 6480 in 3 years and rs 7776 in 4 years interest being compounded annually, find the sum and rate of interest.
solve it
it's urgent
Answer:
The rate of interest is 20% and the sum is $3,750
Step-by-step explanation:
In order to calculate the sum and rate of interest we would have to make the following calculation:
rate of interest= (sum in 4 years-sum in 3 years)*100/sum in 3 years*1
According to the given data we have the following:
sum in 4 years=$7,776
sum in 3 years=$6,480
Therefore, sum in 4 years-sum in 3 years=$7,776-$6,480=$1,296
Therefore, rate of interest=$1,296*100/$6,480*1
rate of interest=20%
To calculate the sum we would have to make the following calculation:
FV=PV(1+20%)∧3
$6,480=PV(1,20)∧3
PV=$3,750
Sum is $3,750
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
2 + 2 = 4 - 1 =3 quick maths..... NOT A QUESTION BUT WHOEVER ANSWERS FIRST GETS BRAINLIEST
Answer:
That is correct
Step-by-step explanation:
yes sir you are corret
A record store owner assesses customers entering the store as high school age, college age,
or older, and finds that among all customers 30%, 50%, and 20% respectively, fall into these
categories. The owner also found that purchases were made by 20% of high school age
customers, by 60% of college age customers, and by 80% of older customers.
(a) Find the probability that a randomly chosen customer will make a purchase?
(b) If a customer makes a purchase, what is the probability that this customer is of college
age?
Step-by-step explanation:
(a) P = (0.3)(0.2) + (0.5)(0.6) + (0.2)(0.8)
P = 0.52
(b) (0.5)(0.6) = 0.3
P = 0.3 / 0.52
P = 0.58
If a customer makes a purchase, then the probability that this customer is of college will be 0.58
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers.
(a) the probability that a randomly chosen customer make a purchase will be;
P = (0.3)(0.2) + (0.5)(0.6) + (0.2)(0.8)
P = 0.52
(b) if a customer makes a purchase, then the probability that this customer is of college will be;
(0.5)(0.6) = 0.3
P = 0.3 / 0.52
P = 0.58
Learn more about probability here;
https://brainly.com/question/11234923
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If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answer:
B'(0,-2)
Step-by-step explanation:
the coordinates of B (-5,0)
the translation is(x+5,y-2)
B' : (-5+5,0-2)
B'(0,-2)
What is 4sqrt7^3 in exponential form?
Answer:
[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]
Step-by-step explanation:
[tex]4 (\sqrt{7} )^3[/tex]
Square root can be written as a power.
[tex]4(7^{\frac{1}{2} })^3[/tex]
Multiply the exponents.
[tex]4(7^{\frac{3}{2} })[/tex]
Answer:
A (7^3/4)
Step-by-step explanation:
ed 2020
What is the radius of a circle that has a circumference of 3.14 meters?
Answer:
Hey there!
Circumference of a circle=0.5[tex]\pi[/tex]r
3.14=0.5[tex]\pi[/tex]r
1=0.5r
r=2
Hope this helps :)
Answer:
1/2 meter
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c= pi* 2r
We know that the circumference of the circle is 3.14 meters. Therefore, we can substitute 3.14 in for c.
3.14= pi* 2r
We want to find out what r, or the radius is. To do this, we must get r by itself.
First, divide both sides of the equation by pi, or 3.14. We divide because 2r is being multiplied by pi, and division is the inverse of multiplication.
3.14= pi* 2r
3.14/3.14=3.14* 2r/3.14
3.14/3.14=2r
1=2r
Next, divide both sides by 2. We divide because 2 and r are being multiplied, and the inverse of division is multiplication.
1/2=2r/2
1/2=r
0.5=r
The radius of the circle is 1/2 or 0.5 meters.
Velocity of a Car The velocity of a car (in feet per second) t sec after starting from rest is given by the function f(t) = 11 t (0 ≤ t ≤ 30). Find the car's position, s(t), at any time t. Assume that s(0) = 0. s(t) =
Answer:
s(t) = 11t²/2Step-by-step explanation:
Velocity is defined as the rate of change in displacement of a body. It is expressed mathematically as v = change in displacement/time
v(t) = ds(t)/dt
ds(t) = v(t)dt
integrating both sides;
s(t) = [tex]\int\limits v(t)dt[/tex]
Given the velocity function f(t) = 11t, the car's position (displacement) is expressed as s(t) = [tex]\int\limits 11t\ dt[/tex]
s(t) = 11t²/2 + C
at the initial point, s(0) = 0 i.e when t = 0, s(t) = 0. The resulting equation becomes;
0 = 11(0)²/2+ C
0 = 0+C
C = 0
To find the car's position, s(t), we will substitute C = 0 into the equayion above;
s(t) = 11t²/2 + 0
s(t) = 11t²/2
Hence s(t) = 11t²/2 is the required position of the car in terms of t.
Using an integral, it is found that the car's position, at any time t, is given by:
[tex]s(t) = \frac{11t^2}{2}[/tex]
The velocity of the car is modeled by the following function:
[tex]f(t) = 11t, 0 \leq t \leq 30[/tex]
The position is the integrative of the velocity, hence:
[tex]s(t) = \int f(t) dt[/tex]
[tex]s(t) = \int 11t dt[/tex]
[tex]s(t) = \frac{11t^2}{2} + K[/tex]
In which the constant of integration K is the initial position. Since the initial position is [tex]s(0) = 0[/tex], the constant is [tex]K = 0[/tex], and hence, the car's position, at any time t, is given by:
[tex]s(t) = \frac{11t^2}{2}[/tex]
A similar problem is given at https://brainly.com/question/14096165
Find the GCF of 207c^3 and 108c^2
Answer: 9c²
Step-by-step explanation:
To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.
207c³ 108c²
∧ ∧ ∧ ∧
9·23 c·c·c 9·12 c·c
∧ ∧ ∧
3·3 3·3 3·4
∧
2·2
207c³: 3·3·23 c·c·c
108c²: 2·2·3·3·3·4 c·c
GCF = 3·3 c·c
= 9c²
The GCF of 207c^3 and 108c² is 9c²
Given the expressions [tex]207c^3 \ and \ 108c^2[/tex]
We are to find the GCF of both terms
First, we need to get the factors as shown::
207c³ = 9 * 23 * c² * c
108c² = 9 * 12 * c²
From the factors, we can see that 9 and c² are common to both terms:
The GCF of 207c^3 and 108c² is 9c²
Learn more here: https://brainly.com/question/21612147
of the 1248 students enrolled 24% did not like the new mascot design. what is the mean of this binomial distribution
A. 299.5
B. 948.5
C. 17.3
D. 300.3
Answer: A. 299.5
Step-by-step explanation:
1248 · 24%
1248 · 0.24=299.50
Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 7 inches shorter than the length of the mat and the hypotenuse is 1 inches longer than the length of the mat, what is the length of the mat?
Answer: length = 12
Step-by-step explanation:
Use Pythagorean Theorem: length² + height² = hypotenuse²
length = L
height = L - 7
hypotenuse = L + 1
L² + (L - 7)² = (L + 1)²
L² + L² - 14L + 49 = L² + 2L + 1
2L² - 14L + 49 = L² + 2L + 1
L² - 14L + 49 = 2L + 1
L² - 16L + 49 = 1
L² - 16L + 48 = 0
(L - 4)(L - 12) = 0
L - 4 = 0 L - 12 = 0
L = 4 L = 12
Input L = 4 and L = 12 to find the height:
Height = L - 7 height = L - 7
= 4 - 7 = 12 - 7
= -3 = 5
↓
negative height is not valid
So, the only valid solution is L = 12
A type of probability distribution that shows the probability of x successes in n trials, where the probability of success remains the same from trial to trial, is referred to as a(n) ______.
Answer: Binomial distribution
Step-by-step explanation:
The binomial appropriation is a likelihood circulation that sums up the probability that a worth will take one of two free qualities under a given arrangement of boundaries or suspicions. The hidden suspicions of the binomial dispersion are that there is just a single result for every preliminary, that every preliminary has a similar likelihood of achievement, and that every preliminary is totally unrelated, or autonomous of one another.
The graph for the equation y=-2x+1 is shown below.
ch
-3
-2 -2
х
-2
-3
If another equation is graphed so that the system has no solution, which equation could that be?
O y=-2(x-3)
Hark this and return
Save and Exit
Next
Submit
Answer:
Step-by-step explanation:
Given the equation y=-2x+1 and given another equation y=mx+b in order for us to have no solution we must guarantee that both lines do not intersect. Recall that m is the slope of the second equation and b the y-intercept. To guarantee that both lines don't intersect, they must be parallel. To have this result, we must have that they have the same slope but different y intercept. That is take m = -2 and b any value different to +1. For example, the b = 6. So
y = -2x+6 = -2(x-3) is another equation that gives no solution to the system.
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
hope this is the answer that you are looking for :)
A pianist plans to play 5=pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second etc. to create a good flow. How many different recital programs are possible?
Answer:
2432902008176640000 programs are possible using 20 distinct (different) songs.
Step-by-step explanation:
There are 20 choices for the first song, 19 choices for the second, ...1 song for the last for a total of
N = 20*19*18*...*3*2*1 = 20!= 2432902008176640000 programs
The number 20! is the number of permutations for 20 distinct objects put in order.
20! is pronounced as 20 factorial.
Example: factorial of 5 is 5*4*3*2*1 = 120
Answer:
20*19*18*17*16=1 860 480 different programs
Step-by-step explanation:
So there are 20 pieces total and each of them can be first.
Each of residual 19 can be the second
Each of residual of 18 can be the third
Each of residual 17 can be the fourth
Each of residual 16 can be the fifth
Total amont of possible different programs ( the order of the pieces matters)
is : 20*19*18*17*16=1 860 480 different programs
Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation:
helpppppppppppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
Hope this helps
Can someone please help me!
Part B
In the right triangle shown below, are any altitudes shown? Does this lead to any generalizations about right triangles?
Explain your answer.
Answer:
In the right triangle, either leg could be considered as the heigh
Step-by-step explanation:
In the right triangle, if you have the length of the two legs, the triangle is already defined, the two legs are the base and the height (no matters the way you choose the order, either AB could be defined as the base or as the height, and if you decide to call AB the base then you necessarily need to take AC as the height.
As can be seen, the area of the triangle and its hypothenuse will be the same.
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
A sample size of 2080 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that [tex]\pi = 0.6[/tex]
How large of a sample size is required?
We need a sample of n.
n is found when [tex]M = 0.025[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]
[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]
[tex]n = 2079.3[/tex]
Rounding up
A sample size of 2080 is needed.
What is the answer for x? (3x-3)° [6(x-10)]
Answer:
x = 19
Step-by-step explanation:
The angles are vertical angles which means they are equal
3x-3 = 6(x-10)
Distribute
3x-3 = 6x-60
Subtract 3x from each side
3x-3 -3x = 6x-60-3x
-3 =3x-60
Add 60 to each side
-3+60 =3x-60+60
57 = 3x
Divide by 3
57/3 = 3x/3
19 =x
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
If g(x)=f(1/3x) which statement is true
Answer:
the graph of g(x) is horizontally stretched by a factor of 3
Step-by-step explanation:
A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the lighthouse.
Answer: 34.64 m
Step-by-step explanation:
Given: A boat is 60 m from the base of a lighthouse.
The angle of depression between the lighthouse and the boat is 37°.
By using trigonometric ratios :
[tex]\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}[/tex]
here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m
[tex]\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64[/tex]
Hence, the lighthouse is 34.64 m tall.
The Coffee Counter charges $8 per pound for Kenyan French Roast coffee and $7 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $7.30 per pound?
Answer:
Kenyan French Roast coffee x=6
Sumatran coffee y=14
Step-by-step explanation:
x+y=20 blend coffee
8x+7y=7.3(20) selling price
x+y=20 ⇒ x=20-y
substitute in the equation:
8x+7y=7.3(20)
8(20-y)+7y=7.3(20) for 20 pound blend
160-8y+7y=146
-y=146-160
y=14 pond
x+y=20
x=20-14=6
check : 14*7+6(8)=146/7.3=20 pound
The price of the Kenyan French Roast coffee is $6 and the price of Sumatran coffee is $14.
Two equations can be derived from the question:
8x + 7y = 20(7.3)
8x + 7y = 146 equation 1
x + y = 20 equation 2
Where: x
x = Kenyan French Roast coffee
y = Sumatran coffee.
To determine the value of y, multiply equation 2 by 8
8x + 8y = 160 equation 3
Subtract equation 1 from 3
y = 14
Substitute for y in equation 2
x + 14 = 20
x = 20 - 14
x = 6
To learn more about simultaneous equations, please check: brainly.com/question/23589883
will give brainly and thanks
Answer:
x = 39
Step-by-step explanation:
The two angles will be equal when the lines are parallel
4x-24 = 3x+15
Subtract 3x from each side
4x-24-3x = 3x+15-3x
x-24 = 15
Add 24 to each side
x-24+24 = 15+24
x = 39
Answer:
x=39
Step-by-step explanation:
Since these are alternate interior angles they should be set equal to each other so
4x-24=3x+15
Now simplify to get...
x=39
h(x)=-4+16 find x when h(x)=48 Plz don't say it is incomplete
Answer:
x = -8
Step-by-step explanation:
When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!
Think of it like saying y = -4x + 16, y = 48.
48 = - 4x + 16
32 = - 4x
8 = -x
Divide by -1 both sides.
-8 = x
A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies:
Grade A B C D E
Frequency 18 20 28 23 11
Compute the value of the test statistics. Do the data provide enough evidence to support the professor’s claim?
Answer:
clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.
Step-by-step explanation:
lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.
first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.
in particular lets take grade A proportional to grade B which implies that 18:20
clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.
Find m<1. Triangle Angle-sum theorem
Answer:
m<1 = 50
Step-by-step explanation:
We can first find the angle next to 140, by doing 180 - 40 = 40.
Now that we know that one of the triangles angle is 40, we also know that there's a 90 degree angle, so we can do:
180 - 90 - 40 = 50
So m<1 = 50
A student's course grade is based on one midterm that counts as 10% of his final grade, one class project that counts as 5% of his final grade, a set of homework assignments that counts as 45% of his final grade, and a final exam that counts as 40% of his final grade. His midterm score is 60, his project score is 80, his homework score is 75, and his final exam score is 78. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answer:
His overall final score is a 73, which means that that student recieved a letter grade of a C.
Step-by-step explanation:
First, we are finding the mean of the scores to average everything out.
So, start by adding up all the scores given: 60+80+75+78=293.
Then, divide that sum by the number of scores given: 293/5=73.25, or rounded to a whole number is a 73.
In most schools, a 73 is a C, so this students letter grade for this course is a C.