jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, how much did she earn in all
?
Answer:
jenny earned a total of $103.05.
Step-by-step explanation:
jenny charges 9.15 an hour to babysit todllers and 7.4 an hour to babysit school -aged children. if jenny babysat toddlers for 9 hours and school -aged childrenfor 6, she earned in all 83.55.
after fitting a linear regression model to a dataset, the model's slope and intercept are -3 and 0 respectively. now, if we change our independent variable by adding 4.5 units to x, what is the absolute value of the change in the predicted value of dependent variable y?
The absolute value of change in the predicted value of dependent variable Y is 18.
Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.
Slope = b = -4
Intercept = a = -2.8
So, the equation of the regression line is
y = a + bx
y = -2.8 - 4x ...Equation 1
Now suppose the value of x is changed by adding 4.5
i.e. put x = x + 4.5
So,
y = -2.8 - 4(x + 4.5)
y = -2.8 -4x - 18 ...Equation 2
Comparing 1 and 2 ,
We get the predicted value of dependent variable Y as 18
Therefore The absolute value of change in the predicted value of dependent variable Y is 18
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Use Product of Powers Property. Property. Do You Know How? 4. A bacteriologist estimates that there are 5.2 x 104 bacteria growing in each of 20 petri dishes. About how many bacteria in total are growing in the petri dishes? Express your answer in scientific notation.
There are in total 1.04 x 10^6 bacteria that are growing in the petri dish.
Given that, there are 5.2 x10^4 bacteria in each 20 petri dish, we have to multiply 5.3x10^4 by 20, get the total bacteria in all 20 petri dish.
5.2 x10^4x 20
= 1,040,000
We have to write this in scientific notation.
The goal of scientific notation is to make it simple for scientists to write extremely large or extremely small numbers.
Since it always follows this notation, calculating scientific notation for a positive integer is straightforward:
a x 10^b
1.040000
1 is a, there are 6 digits right to the decimal point.
a=1.04
b=6
The scientific notation for total bacteria in 20 petri dish is 1.04 x 10^6.
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What is the solution set for 5x−5=15, given the replacement set {0, 1, 2, 3, 4}?
Responses
A: x = 4
B: x = 3
C: x = 2
D: x = 1
E: x = 0
Answer: A: x=4
Step-by-step explanation:
5(4)-5=15
20-5=15
15=15
Dan is 12 4/5 years old. Karina is 1 1/6 years older than Dan and Jane is 1 1/3 years older than Karina. How old is Jane?
The age of Jane based on the information is 10 3/10 years.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
In this case, Dan is 12 4/5 years old, Karina is 1 1/6 years younger than Sarah and Jane is 1 1/3 years younger than Greg
The age of Jane will be:
= 12 4/5 - 1 1/6 - 1 1/3
= 12 24/30 - 1 5/30 - 1 10/30
= 12 24/30 - 2 15/30
= 10 9/30
= 10 3/10
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A right triangle has a leg length of square root of 7 and a hypotenuse length of 4. Determine the length of the other leg of the right triangle.
square root of 57
square root of 49
8
3
The length of the other leg of the right angles triangle is 3. Option D
How to determine the length of the sideThe Pythagorean theorem states that the square of the hypotenuse side is equal to the square of the other two sides in a right angled triangle.
We have;
a² = b² + c²
Where;
a is the hypotenuseb is the opposite sidec is the adjacent sideNow, substitute the values
4² = (√7)² + c²
Find the square values
16 = 7 + c ²
collect like terms
c² = 9
Find the square root of both sides
c = 3
Hence, the value is 3
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Answer:The length of the other leg of the right angles triangle is 3. Option D
Step-by-step explanation:
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $ each. She must deliver all the tee-shirts in days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
The equation to represent total amount of money that she receives for the tee shirts in terms of number of machines is 2800*n*(200 - n) .
In the question ,
it is given that
the cost of 1 tee - shirt = $14
total days required to deliver the tee shirt = 20
number of tee - shirts that a machine can produce = 200 per day
let the number of machines = n
so the number of days require to set up the machines = n
hence all the machine will work for = (20 - n) days
1 machines will produce 200(200 - n) tee shirts
n machines will produce = 200n(200 - n) tee shirts in the remaining (20 - n) days .
the selling price of 1 tee shirt is = $14
So, the total money M that she will receive is = 14*200*n*(200 - n)
= 2800*n*(200 - n)
Therefore , The equation to represent total amount of money that she receives for the shirts in terms of number of machines is 2800*n*(200 - n) .
The given question is incomplete , the complete question is
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money( M ) she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
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Bo fell asleep 84% if the total length was 600 miles how many miles had they travel when bo fell asleep
The total distance traveled when Bo fell asleep is 504 miles.
What is the distance traveled?
The path taken by an object to move from a starting point to an ending location in a specified amount of time with a specific velocity is known as the distance traveled.
Given, the total length of distance = 600 miles
Bo fell asleep = 84%
Let 'x' be the distance traveled.
Then, according to the question
x = 84% of 600 miles
or, x = [tex]\frac{84}{100} * 600[/tex]
or, x = 84*6
or, x = 504 miles
Hence, the total distance traveled when Bo fell asleep is 504 miles.
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What is the distance between -15 and 10
1. If a circle is centered at (5, -7) and goes through the point (-3, -1), what is the radius?
2. Why do we prefer the standard form for the equation of a circle over the general form?
Answer: r = 11.3
Step-by-step explanation:
Standard form : (x-h)2 + (y-k)2 = r2
(h,k) = (5,7)
(x,y) = (-3,-1)
r2 = (-3-5)2 + (-1-7)2
r2 = [tex]-8^{2} + -8^{2} = 64 + 64 = 128\\r = \sqrt{128} = 11.3[/tex]
When coordinates of the center of the circle and a point on the circle are known, Standard form is the one to use.
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The compound interest compounded at a rate of 3% quarterly for 5 years is $15,095.39
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeSubstituting the values into the equation given;
A = 13000(1 + 0.03/4)^4 * 5
A = 13000(1.0075)^20
A = $15,095.39
The amount at the end of 5 years is $15,095.39
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Find the exact value of the trigonometric function given that in u = − 8 17 and co v = − 9 41. (Both u and v are in Quadrant III. ) ec(v − u)
Answer:
343
Step-by-step explanation:
Triangles acd and bcd are isosceles. Angle bac has a measure of 18 degrees and angle bdc has a measure of 48 degrees. Find the measure of angle abd.
The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees
What are isosceles triangles?
Isosceles triangles are triangles that have two sides equal in measurement.
Main Body:
From the given diagram;
∠BAC = 18 degrees
∠BDC = 48 degrees
Required angle : ∠ABD
From the diagram, ∠DAB = ∠BAC = 18 degrees
Also, ∠ADC + ∠ACD + ∠DAC = 180
Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes
∠ADC + ∠ADC + ∠DAC = 180
2∠ADC + ∠DAC = 180
2∠ADC = 180 - 36
2∠ADC = 144
∠ADC = 144/2
∠ADC = 72 degrees
This means that ∠ADB = 72 - ∠BDC
∠ADB = 72 - 48
∠ADB = 24 degrees
Get the required angle ABD
From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180
∠ABD + 24 + 18 = 180
∠ABD + 42 = 180
∠ABD = 180 - 42
∠ABD = 138 degrees
Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.
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What is meant by the term sister chromatids?.
When chromosomal DNA replication occurs, two identical copies of a chromosome that are linked by a common centromere form a sister chromatid.
Describe DNA.DNA, commonly referred to as deoxyribonucleic acid, is the genetic material carried by humans and virtually all other organisms. A person's cells have almost the same DNA.
What components makes up DNA?DNA are made molecular building blocks which are known as the nucleotides. These building blocks consist of a phosphate group, a sugar group, and one of four distinct nitrogen bases. To build DNA strands, nucleotides are linked together into chains with the phosphate and sugar groups swapping positions.
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-3.9 + v < -5.2 Solve the inequality for v.
Simplify your answer as much as possible.
Answer:
v<-1.3
Step-by-step explanation:
Add 3.9 to -5.2
v<-1.3
Hope this helped!
Evaluate.
(2/3)4
Enter your answer by filling in the boxes.
??$$
The value of the expression (2/3)4 is 8/3.
Expression:
An expression also known as algebraic expression consists of unknown variables, numbers and arithmetic operators. And it does not contain any equality or inequality symbols.
Given,
Here we have the expression (2/3)4
Now, we have to evaluate the expression to find the solution for this one.
In order to get the solution for this expression,
We have to rewrite the given expression like the following form,
=> (2/3) x 4
Now, we have to multiply 4 with the numerator, then we get,
=> 8/3
Therefore, the solution of this expression is 8/3.
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Parking Lot Design. A rectangular parking
lot is 50 ft longer than it is wide. Determine the
dimensions of the parking lot if it measures 250 ft
diagonally.
The dimensions x and x+50 are 150 ft by 200 ft. When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.
How to calculate the dimensions of the parking if it measures 250 ft diagonally?When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.
If you draw a diagonal, you have 2 right triangles, each with leg lengths of x and x + 50.
The diagonal is the hypotenuse, h = 250
Using Pythagorean theorem:
X² + (x+50)² = 250²
x² + x²+ 100x + 2500 = 62500
2x²+ 100x - 60000 = 0
All are even, so factor out a 2:
x² + 50x - 30000 = 0
From quadratic equation: x = [-50±√(50²-4(1)(-30000))]/(2(1))
x = (-50 ± 350)/2
We can disregard the negative so
x = (-50 + 350)/2 = 300/2 = 150 ft
The dimensions x and x+50 are 150 ft by 200 ft
The complete question is: A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if the diagonal distance from corner to corner of the lot is 250ft.
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Are the lines perpendicular? x=3 and y=5
A. Yes, their slopes are negative reciprocals
B. No, their slopes are not negative reciprocals
Answer: A. Yes, their slopes are negative reciprocals
Step-by-step explanation:
x=3 is a vertical line where every y value lands on x=3. (Undefined slope)
y=5 is a horizontal line where every x value lands on y=5 (Zero slope)
Even though the slopes are not numbers they can still be negative reciprocals. The lines are indeed perpendicular and thus the slopes are negative reciprocals. The relationship between undefined slopes and zero slopes is negative reciprocals because 0/1 cannot be inversed because anything divided by 0 is undefined.
the question is in the image
Answer:
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Step-by-step explanation:
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Giving brainliest! answer quickly.
The expression on the left side of an equation is shown below.
3 (x + 1) + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
Group of answer choices
2 (x + 6) + x
4(x – 3) – x
3 (x + 4)
3 (x + 1) + 9 x
Answer:
The expression "2(x + 6) + x" would make the equation unsolvable (i.e., no solution),
Step-by-step explanation:
This initially appears to be an odd question, since one might imagine that there would always be a solution for x, no matter what is put into the "box." But lets take a look and see what the possible solutions look like when compared to the original equation. First, rearrange the reference equation so that we can better compared it to the answer options:
3 (x + 1) + 9 = box
3x + 3 + 9 = box
3x + 12 = box
3(x + 4) = box
Now look through the answer options and evaluate how, or if, they may be able to prevent us from finding an actual value or x::
-------------------------
Option[Box] Reformatted Complete Equation Unsolvable?
2(x + 6) + x 3x + 12 3(x + 4) = 3x + 123x + 12 = 3x +12
0 = 0 YES*
4(x – 3) – x 11x - 12 3(x + 4) = 11x - 123x + 12 = 11x - 12
-8x = -24
x = 3 NO
3(x + 4) 3(x + 4) = (x+4)2(x+4) = 0
2x = -8
x = -4 NO
(x + 1) + 9x 10x + 1 3(x + 4) = 10x+1 3x+12 = 10x + 1 -7x = -11 x = (11/7) NO
* The YES answer means that this expression would make the answer unsolvable. Note that the expressions on both sides of the equation are equal. So there is no one answer. Any choice of a value for x will always be a valid solution. A singkle value is not possible with this equation.
A cone has a volume of 8π cubic feet and a height of 6 feet. What is the radius of the base?
Answer:
r≈1.13ft
Step-by-step explanation:
hope this helps <333
Three quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls?.
The ratio of boys to girls of the junior members of a tennis club is 1 : 3.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Three-quarters of the junior members of a tennis club are boys.
Assuming the total no. of boys and girls is 1.
∴ 3/4 members are boys and (1 - 3/4) = 1/4 are girls.
So, the ratio of boys to girls is 1/4 : 3/4 which is equal to 1 : 3.
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In a toy store the ratio of legos to board games is
9:6. If the store has 24 legos, how many board games
are in the store?
The store has 16 board games
What are equivalent ratios?
The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.
Let x = number of legos
Let y = number of board games
Given ratio: 9:6= 9/6
x/y = 9/6
substitute x=24
24/y=9/6
Do cross multiplication
(6*24)/9=y
16=y
or
y=16
So, the store has 16 board games
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40% of what number is 46?
The number is 115.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = [tex]\frac{a}{b}[/tex] x 100
We have,
Number = M
40% of M = 46
[tex]\frac{40}{100}[/tex] x M = 46
M = (46 x 100) / 40
M = 115
Thus,
The number is 115.
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3) What is the slope of the line from the following points (-3, -2) and (1, -7) ? (Please show your work for your full points)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{1 +3} \implies \cfrac{ -5 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{5 }{ 4 } \end{array}}[/tex]
HELP PLEASE 100 POINTS
Answer: ∠1 = 90°
Step-by-step explanation:
There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.
First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).
89° = 51° + ∠3
∠3 = 38°
Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.
90° = ∠3 + ∠2
90° = 38° + ∠2
∠2 = 52°
Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.
180° = 38° + ∠1 + ∠2
180° = 38° + ∠1 + 52°
180° = 90° + ∠1
∠1 = 90°
Answer:
90
Step-by-step explanation:
I started by finding angle 5
180 - 89 = 91 Supplemental angles
Then I found angle 3
The sum of the interior angles of a triangle is 180
180-89-91 = 38
Angle2 and 3 are complementary angles
90- 38 =52
the sum of the interior angles of a triangle is 180
Angle 1
180 - 52 - 38 = 90
hank needs to pack 100 golf balls into 8 boxes. each box must contain an equal number of golf balls. how many golf balls does he have left over?
Answer: 4
Step-by-step explanation:
100/8 = 12 golf balls in each box
8*12 = 96 golf balls are used
100-96= 4 gold balls left
your help would be nice please I don't understand
Answer:
y=1.5x-3
Step-by-step explanation:
(0,-3) => x=0, y=-3
(2,0) => x=2, y=0
y=ax+b
-3=a*0+b
0=2*a+b
-3=b
0=2a+b
2a-3=0
2a=3
a=1.5
b=-3
y=1.5x-3
Answer:
[tex]y = \dfrac{3x}{2} -3[/tex]
Step-by-step explanation:
Before we identify the equation of the line in slope intercept form, we must identify the slope intercept form equation. The slope intercept form equation is y = (m)x + (b) ⇒ m = slope of line; b = y-intercept of line.
To identify the equation of the line shown in slope intercept form, according to the slope intercept form equation, we need to identify the slope of the line and the y-intercept of the line. The slope of a line is the rate of a line, which advances up/down/side-to-side at a constant rate. The y-intercept of a line is the intersection of the line at the y-axis.
There is a specific formula for identifying the slope:
[tex]\boxed{\text{Slope} = \dfrac{\text{y coordinate of 2nd point - y coordinate of 1st point}}{\text{x coordinate of 2nd point - x coordinate of 1st point}}}[/tex]
Some facts about slope: The slope of a line will also depend on the graph. If the graph ascends upward to somewhere in Quadrant 1 or 2, the slope of the line will be positive. If the graph descends downward to somewhere in Quadrant 3 or 4, the slope will be negative. If the line horizontal and it passes perfectly through the x-axis, the slope of the line is 0. If the slope of the line is vertical, then the slope will be undefined.
Location of plotted points: First point: (0, -3); Second point: (2, 0)
Let us now identify the x and y coordinates of the plotted points:
[tex]\boxed{\text{y-coordinate of 2nd point = 0; y-coordinate of 1st point = -3}} \\ \boxed{\text{x-coordinate of 2nd point = 2; x-coordinate of 1st point = 0 }}[/tex]
Plug the coordinates into the slope formula to determine the slope:
[tex]\implies {\text{Slope} = \dfrac{\text{0 - (-3)}}{\text{2 - 0}}} = \dfrac{0 + 3}{2} = \dfrac{3}{2}[/tex]
Plug the slope of the line into the slope intercept form equation:
[tex]\implies y = (m)x + (b)[/tex]
[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (b)[/tex]
[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]
Let us plug any point (that is on the line) for x and y. This will help us find the y-intercept (b). I will plug in the first point because it is my preference.
[tex]\implies y = \dfrac{3(x)}{2} + b[/tex]
[tex]\implies -3 = \dfrac{3(0)}{2} + b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{First point: (0, -3)} \implies x = 0; y = -3]}[/tex]
[tex]\implies -3 = 0 + b[/tex]
[tex]\implies -3 = b[/tex]
Finally, let us substitute the slope of the line and the y-intercept of the line into the slope-intercept form equation. Then, we can simplify both sides of the equation and isolate the y-variable completely on the other side.
[tex]\implies y = (m)x + (b)[/tex]
[tex]\implies y = \huge\text{(}\dfrac{3}{2} \huge\text{)}x + (-3)[/tex]
[tex]\implies y = \dfrac{3x}{2} -3[/tex]
Therefore, the equation of the line in slope intercept form is y = 3x/2 - 3.
find distance between (-5,6) and (8,-4) SHOW WORK PLEASE
Answer:
(3,2)
Step-by-step explanation:
-5+8=3
6-4=2
(3,2)
The Playhouse Concert Hall has 523 seats. The Pink Ladies rock band is holding a concert there and charging $35.50 for each ticket. If the concert sells out, how much money will the band earn?
The total amount that the band earns when the concert sells out is $18566.50
Given,
Number of seats in The Playhouse Concert Hall = 523
The cost for one ticket charged by The Pink Ladies rock band who holds a concert = $35.50
We have to find the total amount that the band earns when the concert sells out;
Total amount = Number of seats x Cost for one ticket
Total amount = 523 x 35.50
Total amount that the band earn = $18566.5
That is,
The total amount that the band earns when the concert sells out is $18566.50
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