$3 donated_____$120 spent
$1,000 donated__X=$40,000 spent
(1,000*120)/3= 40,000
Answer: The Customers have to spend $4000 in order to raise $1000 for the pet rescue program.
Step-by-step explanation:
Hi, to answer this question we have to write a proportion.
Proportion = money spent / money raised for the pet rescue program
For every $120 that customers spend, $3: 120/3
To raise $100 : x / 100
Where x is the money that customers spent to raise $100 for the pet rescue program.
Solving for x:
120/3 = x /100
(120/3)100=x
x =$4000
3 is less than or equal to 7+g
2≤4 so you have to do that by seeing that 3 iss less that 7
4. (3x² + 3x-2) + (3x² - 5x - 3)
2
Answer:
6x^2-2x-5
Step-by-step explanation:
(3x^2+3x-2)+(3x^2-5x-3)
3x^2+3x^2+3x+(-5x)-2+(-3)
6x^2+3x-5x-2-3
6x^2-2x-5
It takes 12 hours for 7 men to paint a room.
How many men would be needed to paint the room in 3 hours?
28 men are needed to paint the room in 3 hours
Solution:Given that it takes 12 hours for 7 men to paint a room
We are asked to find number of men required to paint the room in 3 hours
Recognize, "paint the room" is 1 task. One job.
7 men -------- 12 hours ------ 1 job
(7/7) = 1 men ------- 12 x 7 (84) ------- same 1 job
The one men is rate is 84 hours to do the job
We can express this as 1/84 jobs per hour, the one-person rate
Now lets find how many men needed to paint the room in 3 hours
Let the required number of men for 3 hours be "a"
The rates of each person is simply additive.
[tex]a \times \frac{1}{84} \times 3 = 1[/tex]
corresponds to rate x hours = jobs and "a" is a variable for how many men
[tex]a \times \frac{1}{28} = 28[/tex]
Thus 28 men are needed to paint the room in 3 hours
please explain, but not to wordy
Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]
Step-by-step explanation:
Solving the expression:
[tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex]
Solving the expression:
We will find factors of the quadratic terms:
[tex]x^2-12x+32\\=x^2-8x-4x+32\\=x(x-8)-4(x-8)\\=(x-4)(x-8)[/tex]
So, factors of [tex]x^2-12x+32[/tex] are [tex](x-4)(x-8)[/tex]
[tex]x^2-10x+16\\=x^2-8x-2x+16\\=x(x-8)-2(x-8)\\=(x-2)(x-8)[/tex]
So, factors of [tex]x^2-10x+16[/tex] are [tex](x-2)(x-8)[/tex]
Placing factors instead of quadratic equation and finding common terms:
[tex]\frac{(x-4)(x-8)}{(x-2)(x-8)}.\frac{6(x-5)}{-5(x-5)}[/tex]
Cancelling the common terms:
[tex]\frac{(x-4)}{(x-2)}.\frac{6}{-5}\\-\frac{6(x-4)}{5(x-2)}[/tex]
So, Solving the expression [tex]\frac{x^2-12x+32}{x^2-10x+16}.\frac{6x-30}{25-5x}[/tex] we get [tex]-\frac{6(x-4)}{5(x-2)}[/tex]
Keywords: Solving Fractions
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Solve for q.
q/18 = 5
q = ___0a
q/18 = 5
q = 18×5
q = 90
Determine if Set of Points is a Function
Nov 25, 1:55:25 PM
Which set of ordered pairs does not represent a function?
{(5, -6), (-1, - 2), (2, –9), (–8, -2)}
{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}
{(-4,2), (-2,8), (-1,6), (5,6)}
{(2,2), (-4,9), (9, -3), (-3, 2)}
NA
Submit Answer
Answer:
{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}
Step-by-step explanation:
In a function, no two points can have the same x-coordinates. In other words, all x-coordinates of the points must be different.
{(5, -6), (-1, - 2), (2, –9), (–8, -2)} : All x-coordinates are different: 5, -1, 2, -8. This is a function.
{(-5, 7), (-4, -9), (–5, – 4), (2, -6)} : Two x-coordinates are the same: -5, -5. This is not a function.
{(-4,2), (-2,8), (-1,6), (5,6)} : All x-coordinates are different: -4, -2, -1, 5. This is a function.
{(2,2), (-4,9), (9, -3), (-3, 2)}: All x-coordinates are different: 2, -4, 9, -3. This is a function.
If the above cat measures 15 inches, how many centimeters (cm) is that, if 1 inch = 2.54 cm.Show how you got your answer please.
Answer:
Step-by-step explanation:
Inch = Cm
1 = 2.54
15 = ?
We have to find out the question mark. So to do this we have to find out how we got from 1 to 15. We did this by multiplying by 15.
Inch = Cm
1 = 2.54
×15
15 = ?
So we must do the same on the other side.
1 = 2.54
×15 ×15
15 = ?
2.54×15=38.1
1 = 2.54
×15 ×15
15 = 38.1
The answer is therefore 38.1cm
Hope this helped!
A park ranger calculated that 60% of the deer they tagged were male. Of the male deer that
were tagged, 20% of them were older than 4 years. They tagged 18 male deer that were
older than 4 years. How many deer did they tag?
A
45
Answer:
They tagged 90 male deer s
Explanation:
Given a park ranger calculated 60% of male deer
Consider the deer they tagged to be x
According to question,
20% of deer were older than 4 years which equals 18
Then, 20% of x = 18
Solving for x,
x = 1800/20
x = 90
So, they tagged 90 male deer
Only question 10. please
Jeremy’s pay is $8.25 per hour. Jeremy worked 78 hours in a month, and the pay statement showed a total of $128.70 in payroll taxes. What was Jeremy’s net income?
Jeremy’s net income was $514.8
Step-by-step explanation:
The given is:
Jeremy’s pay is $8.25 per hourJeremy worked 78 hours in a monthThe pay statement showed a total of $128.70 in payroll taxesWe need to find what Jeremy’s net income was
The net income = total income - taxes
∵ Jeremy’s pay is $8.25 per hour
∵ Jeremy worked 78 hours in a month
- Jeremy's income = the pay for an hour × the worked hours
∴ Jeremy's income = 8.25 × 78
∴ Jeremy's income = $643.5 in a month
∵ There was $128.7 as taxes in his pay statement
∴ The taxes = $128.7
- Substitute the values of his income and the taxes in the
formula of the net income
∵ The net income = total income - taxes
∴ The net income = 643.5 - 128.7
∴ The net income = $514.8
Jeremy’s net income was $514.8
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P(vanilla) =0.3 P(sundae)=0.2 P(vanilla and sundae) =0.15 find the probability that a customer ordered vanilla ice cream given they ordered a sundae. P(vanilla | sundae) =?
Answer:
0.75
Step-by-step explanation:
P(A | B) = P(A and B) / P(B)
P(vanilla | sundae) = P(vanilla and sundae) / P(sundae)
P(vanilla | sundae) = 0.15 / 0.2
P(vanilla | sundae) = 0.75
the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75
Given :
P(vanilla) =0.3, P(sundae)=0.2, P(vanilla and sundae) =0.15
we need to find the probability that a customer ordered vanilla ice cream given they ordered a sundae.
[tex]P(vanilla | sundae)=\frac{P(vanilla \; and \; sundae)}{P(sundae)}[/tex]
Substitute the values and find the probability
[tex]P(vanilla | sundae)=\frac{ 0.15}{0.2}=0.75[/tex]
[tex]P(vanilla | sundae)=0.75[/tex]
the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75
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Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
will give 5 stars and mark brainliest.
Answer:
6.67 feet
Step-by-step explanation:
The situation is as shown in the figure.
ON is the normal to the mirror at the point of incidence O
⇒ ∠BON = ∠DON = 90°
By the laws of reflection: angle of incidence = angle of reflection :
∠AON = ∠CON
⇒ ∠AOB = ∠COD
⇒tan(∠AOB) = tan(∠COD)
⇒[tex]\frac{AB}{OB}[/tex] = [tex]\frac{CD}{OD}[/tex]
⇒[tex]\frac{6}{4}[/tex] = [tex]\frac{10}{x}[/tex]
⇒x = [tex]\frac{40}{6}[/tex] = [tex]\frac{20}{3}[/tex] = 6.67 ft
∴ Distance of the mirror from basketball goal is 6.67 ft
Final answer:
Using the principles of similar triangles, we determine that the mirror is 6 feet from the basketball goal by setting up a proportion between the heights and distances of the triangles formed by the goal and Mumford's line of sight. The mirror is 6 feet from the basketball goal.
Explanation:
To determine how far the mirror is from the basketball goal, we can use the principles of similar triangles. Basketball star Mumford is a six-foot-tall senior forward, meaning he is 6 feet above the ground. The basketball goal is 10 feet tall. If he walks backward four feet, and then he is able to see the top of the basketball goal, we can set up a proportion because the angles of incidence and reflection are equal.
Let's let x be the distance from the base of the basketball goal to the mirror. We then have two similar triangles to work with:
The large triangle with the height of the goal (10 feet) and the base x + 4 feet (distance from the goal to Mumford's eyes).
The smaller triangle with the height from Mumford's eyes to the ground (which is 6 feet because he's a six-foot-tall person) and the base x (distance from the goal to the mirror).
The proportion we set up is:
(Height of basketball goal) / (Distance from goal to Mumford's eyes) = (Height of Mumford's eyes from the ground) / (Distance from goal to the mirror)
10 / (x + 4) = 6 / x
Solving for x gives us the distance from the mirror to the basketball goal:
10x = 6(x + 4)
10x = 6x + 24
4x =24
x = 6
Therefore, the mirror is 6 feet from the basketball goal.
ax−by>c
Solve the following inequality for y, where a, b, and c are positive real numbers.
Show all work and justify each step in the work with mathematical reasoning on the scratchpad.
Answer:
[tex]\large\boxed{y>\dfrac{c-ax}{b}}\\\text{for}\ a>0,\ b>0,\ c>0[/tex]
Step-by-step explanation:
[tex]ax+by>c\qquad\text{subtract}\ ax\ \text{from both sides}\\\\ax-ax+by>c-ax\\\\by>c-ax\qquad\text{divide both sides by}\ b\ (\text{we can, because}\ b>0)\\\\\dfrac{by}{b}>\dfrac{c-ax}{b}\\\\y>\dfrac{c-ax}{b}[/tex]
To solve the inequality ax - by > c for y, you first subtract ax from both sides which gives -by > -ax + c. Then you divide both sides by -b, remembering to flip the inequality sign, which gives y < (ax - c) / b.
Explanation:To solve the inequality ax - by > c for y, you need to isolate y on one side of the inequality.
Subtract ax from both sides to move it away from the left side. The inequality becomes -by > -ax + c.Divide by -b. When you divide or multiply an inequality by a negative number, the direction of the inequality changes. So, the inequality becomes: y < (ax - c) / b.This is the solution for the inequality in terms of y.
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y-2=-(x+7) rewrite in standard form
Answer:
x + y = -5
Step-by-step explanation:
standard form is ax + by = c
equation is y - 2 = -x - 7
Add x to both sides.
x + y - 2 = -7
Now add 2 to both sides.
x + y = -5
I need to write an equation for y = mx + b, The numbers i have are 20-80 and 1-4
Answer:
y = 20x
m = 20 and b = 0
Step-by-step explanation:
For input values of x = 1, output value of y = 20 and for x = 4, y = 80.
Therefore, the equation of this relation can be written as
[tex]\frac{y - 80}{80 - 20} = \frac{x - 4}{4 - 1}[/tex]
⇒ 3(y - 80) = 60(x - 4)
⇒ 3y - 240 = 60x - 240
⇒ y = 20x
Now, y = mx + b is the equation and hence, m = 20 and b = 0 and the actual equation is y = 20x. (Answer)
In order to teach high school, a teacher must have a college degree. Nathan is a high school teacher. Laura concludes that Nathan
must have a college degree.
This is an example of
A.
identifying a hypothesis.
B. inductive reasoning,
C.
identifying a conclusion
D. deductive reasoning.
Answer:
C
Step-by-step explanation:
That is her final answer.
Jayce is a taxi driver
M(n) models Jayce's fee(in dollars) for his nth drive on a certain day.
WHAT DOES THE STATEMENT M(10)= K MEAN??
Answer:
Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.
Step-by-step explanation:
[tex]M(n)[/tex] models Jayce's fee (in dollars) for his [tex]n^{th}[/tex] drive on a certain day.
Substitute [tex]n=10,[/tex] then
[tex]M(10)[/tex] models Jayce's fee (in dollars) for his [tex]10^{th}[/tex] drive on a certain day.
This means Jayce's fee for his [tex]10^{th}[/tex] drive is equal to [tex]K[/tex] dollars.
Answer:
C
Step-by-step explanation:
Jayce's fee for his 10th drive is equal to K dollars.
4. A home purchased for $120,000 in 2012 is sold for $156,000 in 2015. What is the percent
change in the price?
The circle in the figure below has a radius of r and center at C. The distance from A to B is x, the distance from A to D is y, and the length of arc BD is s. Redraw the figure, label it as indicated, and then solve the problem.
If A = 45°, s = 18, and r = 14, find y. (Round your answer to the nearest whole number.)
Answer: y=19
Step-by-step explanation:
The figure of the triangle is attached and we have the following data:
[tex]A=45\°[/tex]
[tex]s=18[/tex] is the length of arc
[tex]r=14[/tex] is the radius
This problem can be solved by the Law of Sines:
[tex]\frac{sin A}{r}=\frac{sin C}{y}=\frac{sin D}{r+x}[/tex]
In order to find [tex]C[/tex], we will use the formula of the length of arc:
[tex]s=\frac{2 \pi r C}{360\°}[/tex]
Then: [tex]C=\frac{360\° s}{2 \pi r}[/tex]
[tex]C=\frac{360\° (18)}{2 \pi (14)}=73.66\°[/tex]
Returning to the Law of Sines:
[tex]\frac{sin A}{r}=\frac{sin C}{y}[/tex]
Finding [tex]y[/tex]:
[tex]y=\frac{sin C r}{sin A}[/tex]
[tex]y=\frac{sin (73.66\°) 14}{sin (45\°)}[/tex]
Finally:
[tex]y=18.99 \approx 19[/tex]
The length of side y is approximately 19 units.
The problem can be approached using the Law of Sines, which relates the angles and sides of a triangle. Given the data:
Angle A (A) is 45°, the side opposite angle A (s) is 18 units, and the radius of the circumcircle (r) is 14 units.
This problem can be solved by the Law of Sines:
sinA / r = sinC / y= sin D/ r + x
To find the length of side y, we can first calculate the measure of angle C (C) by using the formula for the length of an arc:
s= 2πrC/ 360
Then:
C= 360 s/ 2πr
C= 360 (18) / 2π(14)
C= 73.66
Now, we can use the Law of Sines to find the length of side y. The Law of Sines states:
sinA / r = sinC / c
In this case, we want to find side y, which is opposite angle C:
sinA / r = sinC / y
Solving for y :
y = sinCr/ sinA
y= sin ( 73.66 )14/ sin 45
Finally:
y = 18.99 = 19
So, the length of side y is approximately 19 units.
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Distance to your brothers house is 552 miles, and the distance to Disneyland is 736 miles. If it took 12 hours to drive to your brothers house, how long would you estimate the drive to Disneyland to take?
Answer:
I would estimate 61.3
Step-by-step explanation:
I don't think I answered right but I tried
Find the slope of the line passing through (-10,5) , (5,5)?
Answer:
0Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-10, 5) and (5, 5).
Substitute:
[tex]m=\dfrac{5-5}{5-(-10)}=\dfrac{0}{15}=0[/tex]
The slope is equal 0. Therefore given line is a horizontal line.
The equation: y = 5please solve much appreciated
Answer:
i) C; x=y= 80°, ii) B; x= 58°, iii) D; x= 62° and y= 56°, iv) D; none of these are correct.
Step-by-step explanation:
i) Full angle around is 360°
As given one angle is 100°,which means vertically opposite angles are equal to 100°
Now, remaining angle is equal to [tex]360-200= 160°[/tex]
∵ x and y are vertically opposite angle, which means they are equal.
∴x=y= 80°
ii) As we know straight angle is equal 180°
As given one of the angle is 32° and other says, it is a right angle which is equal to 90°.
∴ ∠x= [tex]180-(90+32)= 58°[/tex]
∴∠x= 58°
iii) Full angle = 360°
2∠x = 124° (∵ Vertically opposite angle are equal )
⇒∠x= [tex]\frac{124}{2}[/tex]
∴∠x= 62°
∠x+∠x+∠y= 180° (∵ it is a straight angle)
2∠x+∠y= 180°
⇒[tex]124+ y= 180[/tex]
Subtracting both side by 124
⇒∠y= [tex]180-124= 56°[/tex]
∴∠y= 56°
iv) Full angle= 360°
∴ ∠x+22°+32°+51°= 360°
Subtracting both side by 105
∠x= [tex]360-105= 255°[/tex]
∴∠x= 255°
Which means none of the given option are correct.
801,504 round to the nearest thousand
Answer:
802,000
Step-by-step explanation:
The number in the thousands place is 1, and the number to the right of it is 5. And if the number to the right is greater than or equal to 5 the place value that you are rounding goes up by one.
How would you solve for this? 3x-5 = 1/2x+2x
Answer:
x=10
Step-by-step explanation:
3x-5=1/2x+2x
3x-5=1/2x+4/2x
3x-5=5/2x
3x-5/2x=5
6/2x-5/2x=5
1/2x=5
x=5/(1/2)
x=(5/1)(2/1)
x=10/1
x=10
50 1/2 divided by 1/4 = 202
How are the numbers related?
To solve 50 1/2 divided by 1/4, convert the mixed number 50 1/2 to an improper fraction (101/2), then multiply by the reciprocal of 1/4 (which is 4), resulting in 202. The numbers are related through these multiplication and division steps.
Step by Step Solution:
To understand how the numbers are related in the equation 50 1/2 divided by 1/4, follow these steps:
First, convert the mixed number 50 1/2 to an improper fraction. This is done by multiplying the whole number part by the denominator of the fractional part and adding the numerator. Therefore, 50 1/2 becomes:
50 × 2 + 1 = 101/2
Next, when dividing by a fraction, you multiply by its reciprocal. So, dividing by 1/4 is the same as multiplying by 4/1.
Now multiply the improper fraction 101/2 by 4/1:
(101/2) × (4/1) = 101 × 4 / 2 × 1 = 404/2
Simplify the result by dividing the numerator by the denominator:
404 / 2 = 202
Therefore, the numbers are related through these multiplication and division operations, confirming that 50 1/2 divided by 1/4 equals 202.
Solve for x.
3x – 8 < 23 AND
- 4x + 26 > 6
Answer:
B. x < 5
Step-by-step explanation:
Lets go first with 3x – 8 < 23 then with - 4x + 26 > 6 and after that we put them together. (I will use the < > signs but as I see on the pictures these include the =, being less and greater OR equal).
3x – 8 < 23
Lets sum 8 in both sides:
3x < 23 +8
3x < 31
Now, divide both sides by 3:
3x/3 < 31/3
x < 31/3
Here we found one condition. Lets go with the other inequality for the other condition:
- 4x + 26 > 6
Lest sum 4x in both sides to get a potive x:
- 4x + 26 + 4x > 6 +4x
26 > 6 +4x
Now subtract 6 in both sides
26 - 6 > 6 +4x - 6
20 > 4x
Finally, divide both sides by 4:
20/4 > x or 5 > x (simplifying we get the second)
So, our second condition says that x must be less than 5.
So, putting both conditions together:
x < 5
x < 31/3 = 10.33
So, if x must be less than 5 and less than 10.33, is the same that saying that x mus be less than 5. We con obviate the condition that x must be less than 10.33 as it is included in the other. So our answer is:
x < 5
It is the option B in the image (remember I didnt use the less or equal sign because you didn't included it in the statement).
Mia ordered five DVDs, all at the same price, from an online retailer. There was a shipping charge of $14.50 for the complete order but no sales tax. If Mia’s total charge for her order was $79.45, what was the price of each DVD?
Answer:
$12.99
Step-by-step explanation:
you take $79.45 and subtract it by $14.59 that equals $64.95. Then you take 64.95 and divide it by 5 and your total of each DVD is 12.99
The price of each DVD from online retailer is, $12.99
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
There was a shipping charge of $14.50 for the complete order but no sales tax.
And, Mia’s total charge for her order was $79.45.
Now, The cost of 5 DVD = $79.45 - $14.50
= $64.95
Hence, The price of each DVD from online retailer is,
⇒ $64.95 / 5
⇒ $12.99
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10 students per teacher. Write two ratios to represent this information
5a(-3b)(-2a^2b^3)
what is the answer to this question?
Answer:
(3•5•2a3b4)
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
-15ab • (0 - (2a2 • b3))
Step 2 :
Multiplying exponential expressions :
2.1 a1 multiplied by a2 = a(1 + 2) = a3
Multiplying exponential expressions :
2.2 b1 multiplied by b3 = b(1 + 3) = b4
A movie theater has a seating capacity of 187. The theater charges $5.00
for children, $7.00 for students, and $12.00 of adults. There are half as
many adults as there are children. If the total ticket sales was $ 1356, How
many children, students, and adults attended?
There were 69 children, 83.5 students, and 34.5 adults in attendance at the movie theater.
Explanation:To solve this problem, we can set up a system of equations.
Let's denote the number of children as 'c', the number of students as 's', and the number of adults as 'a'.
From the given information, we have the following equations:
c + s + a = 187 (equation 1)
5c + 7s + 12a = 1356 (equation 2)
We also know that there are half as many adults as children, so we have the equation:
a = (1/2)c (equation 3)
Substituting equation 3 into equations 1 and 2, we can solve for the variables.
Substituting (1/2)c for a in equation 1:
c + s + (1/2)c = 187
(3/2)c + s = 187 (equation 4)
Substituting (1/2)c for a in equation 2:
5c + 7s + 12((1/2)c) = 1356
5c + 7s + 6c = 1356
11c + 7s = 1356 (equation 5)
Now we can solve equations 4 and 5 simultaneously:
Multiplying equation 4 by 11:
(33/2)c + 11s = 2057/2
11c + 7s = 1356
Subtracting the second equation from the first:
(33/2)c - 11c = 2057/2 - 1356
(-1/2)c = -69/2
c = 69
Substituting c = 69 into equation 4:
(3/2)(69) + s = 187
103.5 + s = 187
s = 83.5
Finally, substituting c = 69 and s = 83.5 into equation 3:
a = (1/2)(69)
a = 34.5
Therefore, there were 69 children, 83.5 students (which is not a whole number, so it could be rounded to 84 students), and 34.5 adults (which could be rounded to 35 adults) in attendance at the movie theater.