A daycare center charges $3 per hour for preschool-aged children and $4 per hour for infants and toddlers. This equation represents the number of preschoolers, x, and infants and toddlers, y, at the daycare center in an hour when it earns $180: 3x + 4y= 180. graph the relationship?
Answers
Answer:
answer
Step-by-step explanation:
The required sketch of the curve 3x + 4y = 180 is shown in the graph.
Given that,
A daycare center charges $3 per hour for preschool-aged children and $4 per hour for infants and toddlers. This equation represents the number of preschoolers, x, and infants and toddlers, y, at the daycare center in an hour when it earns $180: 3x + 4y= 180. graph the relationship? is to be determined.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The slope of the given equation is m,
3x + 4y = 180
y = -3/4 * x + 180/4
Comparing above equation with y =mx + c
m = -3/4
So the graph can be sketched as,
Thus, the required sketch of the curve 3x + 4y = 180 is shown in the graph.
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Related Questions
Divide 30 into five parts such that first nad last part are in the ratio 2:3
Answers
To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:
1. Determine the ratio between the first and last parts. In this case, it is 2:3.
2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.
3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.
4. Multiply the value of each part by the respective ratio values to obtain the individual parts:
- First part: 2 * 6 = 12
- Second part: 6
- Third part: 6
- Fourth part: 6
- Last part: 3 * 6 = 18
Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.
estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)
Answers
Answer:
Step-by-step explanation:
To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.
The formula for the volume of a frustum of a pyramid is:
V = (1/3) * h * (A + sqrt(A * B) + B)
Where:
V = Volume of the frustum
h = Height of the frustum (vertical distance between the top and bottom)
A = Area of the top base
B = Area of the bottom base
Given the dimensions provided, we can calculate the areas of the bases:
Area of the top base (A) = 4 m * 4 m = 16 m²
Area of the bottom base (B) = 20 m * 20 m = 400 m²
The height of the frustum (h) is given as 12 m.
Now we can plug these values into the formula:
V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)
Calculating the square root and simplifying:
V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)
V = (1/3) * 12 m * (436 m²)
V = 1744 m³
Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.
Josiah went to the local barber to get his hair cut. It cost $18 for a haircut. Josiah tipped the barber 15%. What was the total cost of the haircut including the tip?
Answers
Answer:
$20.7
Step-by-step explanation:
10
h
+
6
−
5
h
+
3
sorry its weird, you can type it out it wont let me put it normally.
Answers
Answer: 5h+9
Step-by-step explanation:
10h + (-5h)
5h+(6(+3))
How much wrapping is needed to cover a cubed gift box that is 9 inches high? (Include the bow which takes 115 sq. inches.)
Answers
Answer:
601 in²
Step-by-step explanation:
To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow
Area of bow = 115 in²
Surface area of cube shaped box = 6a²
a = side length of cube = 9
Hence,
Surface area of gift box = 6 * 9²
Surface area = 6 * 81 = 486 in²
Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²
Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.
Answers
Given : x³+y³+z³=k , k from 1 to 100
To Find : x, y, and z
Solution:
This Question can have lot of solutions as constraints are very less
there is no information whether x , y & z are integer
+ ve , Real numbers
k = 1
x= 1 , y = 0 , z = 0
x =0 , y = 1 , z = 0
x = 0 , y = 0 , = 1
k=2
x= 1 , y = 1 , z = 0
x =0 , y = 1 , z = 1
x = 1 , y = 0 , = 1
k = 3
x= 1 , y = 1 , z = 3
x = 1 , y = 1 , z = 1
x = 1 , y = 0 , = 1
k = 4
x=∛3 , y = 1 , z = 0
This way we can have so many solution
Easiest :
x³+y³+z³=k,
x = ∛k , y = 0 , z = 0 will satisfy
The possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81
The equation is given as:
\(x^3 + y^3 + z^3 = k\)
To determine the values of k for the equation \(x^3 + y^3 + z^3 = k\), we simply set the values of x, y and z to 1,2,3....... while \(1 \le k \le 100\) is true.
Some possible scenarios are:
When k = 1, we have the following possible values
\((x,y,z) = (0,0,1)\)\((x,y,z) = (0,1,0)\)\((x,y,z) = (1,0,0)\)When k = 2, we have the following possible values
\((x,y,z) = (1,1,0)\)\((x,y,z) = (1,0,1)\)\((x,y,z) = (0,1,1)\)When k = 3, we have the following possible value
\((x,y,z) = (1,1,1)\)Hence, the possible values of k are 1, 2, 3, 8, 9, 10, 17, 24, 43, 62 and 81
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2.1 If an event has a probability that is greater than 0.4, what does it mean?
2.2 What is meant when two events are said to be mutually exclusive?
Answers
Answer:
Step-by-step explanation:
1) i think for the first question any probability greater than 0.4 has more likelihood that it will happen
2) mutually exclusive events are ones that cannot occur at the same time as it's impossible e.g. a single coin toss cannot result in you getting heads and tails
Complete the calculation
5 5 5
5 + 5 + 5 = x 5 = 5 x
Answers
Answer:
29
Step-by-step explanation:
=5+5×5–1(5÷5=1)
Multiplication
=5+25–1(5×5=25)
Addition
=30–1
(25+5=30)
Subtraction
=29
(30-1=29)
Fine the missing length to the nearest 10th
Answers
The value of the missing length to the nearest tenth are;
a. x = 7.5
b. x = 7.8
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
Therefore ;
c² = a²+b²
a. x² = 9²-5²
x² = 81-25
x² = 56
x = √56
x = 7.5 ( nearest tenth)
b. using Pythagoras theorem also!
x² = 6²+5²
x² = 36+25
x² = 61
x = √61
x = 7.8( nearest tenth).
Therefore the value of the missing values are 7.5 and 7.8
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Three grade seven classes were raising money for a
charity. Class A raised $647.53. Class B raised $80.91
more than Class A. Class C raised
as much money
as Class B. How much did the three classes raise in total?
Answers
Answer:
Class A raised $647.53. Since class B raised $80.91 more than class A, then class B raised $728.44. If class B Raised as much money as class C, we multiply $728.44 by 2, and then add $647.53, we get our final answer of $2,104.41
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
Find the surface area of the composite figure.
20 in.
11 in.
5 in.
I
I
19 in
12 in.
12 in.
SA
=
11 in.
5 in.
20 in.
[?] in.2
Answers
The surface area of the composite figure is 2005 in².
To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.
Let's break down the figure into its different parts and calculate the surface area step by step:
Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:
Surface Area of Rectangular Prism = 2lw + 2lh + 2wh
Plugging in the values, we have:
Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²
Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:
Surface Area of Rectangular Prism = 2lw + 2lh + 2wh
Plugging in the values, we have:
Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²
Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:
Surface Area of Rectangle = lw
Plugging in the values, we have:
Surface Area of Rectangle = (11)(5) = 55 in²
Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:
Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle
Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²
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1 1/4 of what number is 36
Answers
Answer:
28.8
Step-by-step explanation:
1 1/4 = 125%
Set up a ratio
36/x = 125/100
Cross multiply
3600 = 125x
28.8 = x
Which expression is equivalent to 5(2+7)
A. 2(5+7)
B. 2+7(5)
C. 5(2)+7
D.5(2)+5(7)
Answers
Answer:
D
Step-by-step explanation:
So 5(2+7) equals 45
A. 2(5+7)=24
B. 2+7(5)=37
C. 5(2)+7=17
D.5(2)+5(7)=45
Only D equals 45
Hope I helped :D
Translate the following into an expression or equation.
Five more than twice a number.
Answers
Answer: 5>x
Step-by-step explanation: hope this right
Answer: 2x+5
Step-by-step explanation:
Five more is adding 5
Twice a number would be 2 times something so we use a variable as "a number"
Select the correct answer.
Which data set has the widest spread?
OA
data set A:3, 1, 2, 6, 7,2,5
O B. data set B: 4, 9, 4, 5, 3, 6, 8
Oc
data set C: 1, 4, 6, 5, 7, 8,5
data set D: 4, 3, 4, 7, 2, 3,1
data set E: 5, 1,4, 2, 6, 9,2
Answers
PLEASE HELP ME 1. A different pool had an area that is of the form
▢ × 102 + ▢ × 101 + 6
and that can be written in the form x3 ,
where x is a whole number.
A) Decide what your number could be.
B) What is the perfect square number that is closest to the number you chose? What would the side length of a square pool with that area be?
C) Estimate the side length of a square pool with the area you chose in part a).
Answers
The solutions to the questions are
The number we are using is 5The perfect square number closest to the area is 1024The estimated side length is 32What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
The number to useThe area expression is given as
Area = ▢ × 102 + ▢ × 101 + 6
From the question, we can use any number
However, this number must be positive
Assume the number is 5
So, we have
Area = 5 × 102 + 5 × 101 + 6
The perfect square number closest to the resultIn (a), we have:
Area = 5 × 102 + 5 × 101 + 6
Evaluate
Area = 1021
The perfect square number closest to this is
Closest = 1024
The estimated side lengthIn (b), we have
Closest = 1024
Rewrite as
Area = 1024
Take the square roots
Length = 32
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8. In a triangle, the three angles are: 60, 11x and 13x degrees. Find the value
of x and plug it in to find the measure of the other two angles. Then classify
the triangle BASED ON ITS ANGLES. *
Answers
Answer:
x=5
Step-by-step explanation:
60+11x+13x =180° (sum of angles in a triangle )
60+24x=180
24x=180-60
24x=120
x=120/24
x=5
Therefore the angles are 60, 55, 65
Which shows that it is a scaleness triangle and an acute angle
If the simple interest on $4,000 for 9 years is $3,240 , then what is the interest rate?
Answers
Answer:
1440000
Step-by-step explanation:
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
Omar shops for a new television. He finds the same television at two different stores priced at $259.99. One store offers a mail-in rebate of $75. At a different store, the television is 30% off the regular price. At which store will Omar receive the better deal? Why?
Answers
Answer:
At the second store. Because 30% Of 259.99 is more than 75$.
Step-by-step explanation:
store 1.
259.99 - 75 = 184.90
stode 2.
259.99 * 30% = 78
259.99 - 78 = 181.99
Question 17 (3 points)
Paul is signing a lease for a two-bedroom apartment that rents for $725/month. How much will Paul pay to move in if
he must pay first and last month's rent and a $500 security deposit?
Answers
Answer:
So If Paul needs to pay for 2 months of rent plus the 500$ in security deposit, then he has to pay 725+725+500=1950
A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
Answers
Answer:
Th computed value of the test statistic is 3.597
Step-by-step explanation:
The null and the alternative hypothesis is as follows:
Null Hypothesis:
\(\mathbf{H_o:}\) the population correlation coefficient is equal to zero
\(\mathbf{H_a:}\) the population correlation coefficient is not equal to zero
The test statistics for Pearson correlation coefficient is thus computed as :
\(t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }\)
where;
r = correlation coefficient = 0.60
n = sample size = 25
So;
\(t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }\)
\(t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }\)
\(t =\dfrac{0.60 *4.796} {0.8}\)
t = 3.597
Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069
Decision Rule:
Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.
Conclusion:
We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.
Janice wins the lottery and takes a lump sum payment. She receives $14,298,120. She places
$10,000,000 into a money market account receiving 10% annual interest compounded monthly,
how much will be in the account after 1 year?
Answers
Answer:
The total compound interest is $1,047,130.76.
Step-by-step explanation:
The amount of the money received after 1 year is $31384283.7672.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = \(A=P(1+\frac{r}{100})^{nt}\).
Given that, principal = $10,000,000, rate of interest =10% and time period = 1 year
Here, A=10,000,000(1+10/100)¹²
= 10,000,000(1.1)¹²
= $31384283.7672
Therefore, the amount of the money received after 1 year is $31384283.7672.
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Consider the set of whole numbers from 1 to 10, inclusive.
List the numbers that meet the condition: less than four and even
Answers
Answer:2
Step-by-step explanation:
Considering the set of whole numbers from 1 to 10, inclusive. The numbers that meet the condition of being less than four and even are:2
To find the numbers that meet the condition of being less than four and even within the set of whole numbers from 1 to 10, inclusive, we can examine each number in the given range and check if it satisfies the condition.
The numbers that meet the condition of being less than four and even are:2
Therefore, the only number that satisfies the condition is 2.
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a van is traveling 1.5 km per minute. How fast is the van traveling in miles per hour?
Answers
Answer:
55.9234
Step-by-step explanation:
1.5*60=90
90km=(x) miles
Answer: 1.5 KPM = 56.25 MPH
Step-by-step explanation:
1.5 divided by 1.6
equals 0.9375
then times that by 60
and get 56.25
Find an ordered pair (x, y) that is a solution to the equation.
3x-y=6
Answers
For example, if we let x = 2, then:
3x - y = 6
3(2) - y = 6
6 - y = 6
-y = 0
y = 0
So, when x = 2, y = 0, and the ordered pair (2, 0) is a solution to the equation 3x - y = 6.
The predecessor of 6,573,800 is
Answers
The predecessor of the number 6,573,800 as given in the task content is; 6,537,799.
What is the predecessor of the number?From the contextual meaning of the word, predecessor, it follows that it means to.find the number right before 6,573,800.
On this note, upon counting of integers, the predecessor of the number 6,573,800 is 6,573,799.
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PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
M= 58 B=64
Step-by-step explanation:
Answer:
M= -1/2 B= 2
Equation: y=-1/2+2
Proportional
Negative Slope
Step-by-step explanation:
Help. Please and thanks.
Answers
Answer:
(2,6)
Step-by-step explanation:
What is a dilation?
A dilation is a type of transformation that resizes an object.
To apply a dilation ( find the coordinates of a point after a dilation ) you must multiply the x and y values of the coordinates by the scale factor
Applying the dilation rule
We want to find the coordinate of vertex B after a dilation with a scale factor of 2. To do so we multiply the x and y value of vertex b by the scale factor or 2
Current coordinates of the triangle :
A(1,1) B(1,3)C(3,1)Coordinates after dilation
A' = (1,1) ===> (1×2,1×2) ===> (2,2)
B' = (1,3) ===> (1×2,3×2) ===> (2,6)
C' = (3,1) ===> (3×2,1×2) ===> (6,2)
The coordinate of the vertex B after the dilation is (2,6)
Suppose you have a jar with 380 marbles that are either red or green. You want to estimate how may marbles in the jar are red without counting all of them. You take four random samples of 16 marbles. After each sample, the marbles are returned to the jar. Choose the best conclusion you can make.
Answers
Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole
Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.
It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.
To calculate the proportion of red marbles in each sample
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