Jordan worked 9 hours as lifeguarding
Jordan worked 6 hours walking dog
given that
Jordan making $13 per hour lifeguarding and $10 per hour walking the dog
last week Jordan earned a total of $177
let x be the number of hours she worked walking the dog
let y be the number of hours she worked as a lifeguard
13y+10x=177 -------- (1)
worked 3 more hour lifeguarding than an hour walking dog
y = 3 + x --------(2)
substitute equation 2 in 1
13(3+x) +10x =177
39+13x+10x = 177
39 + 23x = 177
23x = 177 -39
23x = 138
x = 138/23
x = 6
now substitute x=6 in equation 2
y = 3 + 6
y = 9
9 number of hours he worked lifeguarding last week
6 number of hours he worked walking dog last week
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The sum of 110 and a number
is five times that number
minus 10. What is the
number?
Answer: Let the number = x
5x+10 = 120
Or, 5x = 120 - 10
Or, 5x = 110
Or, x = 110/5
Or, x = 2
Step-by-step explanation:
The larger of two numbers is 12 more than twice the smaller. The larger number is 36. What is the smaller number?
Answer:
The smaller number must be 12
Step-by-step explanation:
Ignoring the second sentence we can make an expression from the question :
x is larger number
y is the smaller number
x = 2y + 12
Now we substitute 36 for x and solve for y :
36 = 2y + 12
Subtract 12 from both sides :
24 = 2y
Divide both sides by 2 :
12 = y
y = 12
The smaller number must be 12.
But let's check :
12 × 2 = 24
24 + 12 = 36
✅
Hope this helped and have a good day
How do you find the Constant of Proportionality in a graph, table or in ordered pairs?
a.divide x by x
b.divide x by y
c.divide y by x
d.divide y by k
The constant of proportionality in a graph, table or ordered pairs is divide y by x
Ising a graph, the constant of proportionality is the constant value of the ratio obtained from two proportional quantities.
How to obtain a constant of proportionality?
The constant of proportionality is the slope of the graph of a straight line.
The slope of a graph of a straight line is determined by:
Slope = rise /run or increase in y/increase in x or decrease in y/decrease in x
In conclusion, rise in y/run in x determines the constant of proportionality.
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Express y in the form axⁿ in the logarithm
[tex] log_{10}y + log_{10}x = 2[/tex]
Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ
The given logarithmic equation is :
log ₁₀y + log ₁₀x = 2
Now we know that: 1 = log₁₀10
∴log ₁₀y + log ₁₀x = 2× log₁₀10
or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)
or, log ₁₀y + log ₁₀x = log₁₀100
we know that log p+ log q = log pq
or, log ₁₀xy = log₁₀100
Now we take antilog on both sides of the equation:
or, xy = 100
or, y = 100 / x
or, y = 100x⁻¹
Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.
A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.
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) a sector of a circle of radius 24 m has an area of 288 m2. find the central angle of the sector in radians.
The Central Angle of the sector in radians is 0.3184 π .
In the question ,
it is given that ,
the radius of the sector = 24 m
the area of the sector = 288 m²
we know that the Area of the sector of the circle is given by the formula
Area = πr²(θ/360)
Substituting the values , we get
288 = (3.14)*(24)²*(θ/360)
θ = (288*360)/((3.14)*(24)²)
θ = 1,03,680/1808.64
θ = 57.32°
converting the angle to radian ,
we get
θ = 57.32° × π/180 radian
= 0.3184 π
Therefore , The Central Angle of the sector in radians is 0.3184 π .
The given question is incomplete , the complete question is
A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .
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1) The USA Today claims that 44% of adults who access the Internet read the international news online. You want to check the accuracy of their claim by surveying a random sample of 120 adults who access the Internet and asking them if they read the international news online. Fifty-two adults responded "yes. " Use a 95% confidence interval to test the newspaper's claim
The accuracy of the USA Today claim about the access the internet read the international news online by adults is 0.089.
We have provided in question that,
adults who access the internet read the international news online is 44% i.e 0.44
this provides the interval ( .344, .522)
Using the estimation formula (E) or margin error
= Z-value √(p (1-p)/n
where, p --> Sample proportion of sucess
1-p = q ----> sample proportion of failure
n ---> sample size
Now, a random sample of 120 adults is considered for survay.
i.e., n= 120 and 52 adults out of 130 are responded "yes" for reading international news online.
so, p = 52/120 = 0.433 and 1-p = q = 1-0.433
= 0.567
Confidence interval to test the newspaper's claim is 95% . Thus, the Z-value for 95% confidence interval is 1.96..
putting the value in above formula we get,
E = 1.96 √0.433×0.567/120 = 1.96√0.2455/120
= 1.96√0.00204 = 1.96× 0.0452 = 0.0889 ~ 0.089
So, accuracy is 0.089 to support the claim of newspaper.
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Which expression represents the total cost for mrs.Alvarez to rent skis for s days and poles for p days
At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off
which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days
If the answer you asked is this:
48s+12p-18 the correct answer
use the following distribution for questions 9-16: p(x,y) y 0 5 10 15 x 0 0.02 0.06 0.02 0.10 5 0.04 0.15 0.20 0.10 10 0.01 0.15 0.14 0.01 question 9: find e[x y]
The value of E[X Y] is 44.25.
According to the question,
E[X] = ∑ x × P(X=x)
=0×P(x=0) + 5×P(x=1) + 10×P(x=2)
= 0+5×(0.49)+10×(0.31)
= 5.55
E[Y] = ∑ y × P(Y=y)
=0×P(x=0) + 5×P(x=5) + 10×P(x=10) + 15×P(x=15)
= 0+5×(0.49)+10×(0.31)+15×(0.21)
= 8.55
Now,
E [X²] = ∑ x² × P(X=x)
= 0²×P(x=0) + 5²×P(x=1) + 10²×P(x=2)
= 0 + 25×0.49 + 100×0.31
= 43.25
E[Y²] = ∑ y² × P(Y=y)
= 0²×P(x=0) + 5²×P(x=5) + 10²×P(x=10) + 15²×P(x=15)
= 0 + 25×0.49 + 100×0.31 + 225×0.21
= 92.25
Therefore , V[X] = E[X²] - {E[X]} = 43.25 - 30.8025 =12.4475
V[Y] = E[Y²] - {E[Y]}² = 92.25 - 73.1025 = 19.1475
E[X Y] = ∑xy P(X=x, Y=y)
= {0×0×P(X=0,Y=0)} + {0×5×P(X=0,Y=5)} + {0×10×P(X=0,Y=0)} + {0×15×P(X=0, Y =15)} + {5×0×P(X=5,Y=0)} + {5×10×P(x=5,Y=10)} + {5×5×P(x=5,Y=5)} + {5×15×P(x=5,Y=15)} + {10×0×P(x=10,Y=0)} + {10×5×P(x=10,Y=5)} + {10×10×P(x=10,Y=10)} + {10×15×P(x=10,Y=15)}
= 0+0+0+0+0 + {50×0.20} +{25×0.15} + {75×0.10} + 0 + {50×0.15} + {100×0.14} + {150×0.01}
= 10 + 3.75 + 7.5 + 7.5 + 14 + 1.5
Hence the final answer is = 41.25
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A retaurant cutomer left $1. 65 a a tip. The tax wa 6% and the tip wa %15 of the cot including tax. What wa the total bill?
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
In the given question we have to find the total bill of the customer.
A retaurant cutomer left $1. 65 a a tip.
The tax was 6% and the tip was 15% of the cost including tax.
The tip was 15%(0.15) of the cost including tax.
Thus 0.15*X= 1.65
Divide both sides of the equation by 0.15.
x = 11
Now 6%(0.06) tax on meal at 11 is
11* 0.06 = 0.66
So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal
The total bill cost = $1.65 + $11+0.66
The total bill cost = 13.31
A retaurant cutomer left $1. 65 a tip. The tax was 6% and the tip was %15 of the cot including tax. Then the total bill is $13.31.
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Researchers at Texas A&M studied the effect of using standing height desks on the energy expended by nine elementary school students. In their paper about the study, they reported descriptive statistics for the nine students. These descriptive statistics were expressed as a mean plus or minus a standard deviation. One such descriptive statistic was the weight of students before using the standing desks, which was reported as 27.0±7.9 kilograms.
Q: What is the standard error of the mean?
The standard error of the mean is 2.63.
What is standard error?The standard error simply means the statistical term that's used to measure the accuracy through which the sample distribution illustrates a population by using the standard deviation.
In this case, the effect of using standing height desks on the energy expended by nine elementary school students was studied.
The standard error will be:
= s /✓n
where
s = standard deviation
n = number of students = 9
= 7.9 / ✓9
= 7.9 / 3
= 2.63
The standard error is 2.63.
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The members of a school club are selling tickets for a fundraiser. The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day.
- On the first day, the members earned 90% of their daily goal.
- On the second day, the members earned 6% more than their daily goal.
- On the third day, the members earned 14% less than their daily goal.
How much money, in dollars, did the members earn from ticket sales on all three days?
(please answer someone i need to ace math)
Answer:
Step-by-step explanation:
The goal for the fundraiser is to earn $50.00 each day
90% of 50= $45
106% of 50=$53
86% of 50=$43
after the three days they earned:
45+53+43=$141
Members earn $141 from ticket sales on all three days.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
The members of a school club are selling tickets for a fundraiser.
The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day.
1).
On the first day, the members earned 90% of their daily goal.
90% of 50
= 90 x 50 / 100
= 4500/100
= $45
2).
On the second day, the members earned 6% more than their daily goal.
That means,
50 + 6% of 50
= 50 + 6 x 50 / 100
= $53
3).
On the third day, the members earned 14% less than their daily goal.
That means,
50 - 14% of 50
= 50 - 14 x 50 / 100
= $43
The total earning = $45 + $53 + $43
= $141
Therefore, $141 is the total earning.
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The perimeter of a park is 10 km . A wall is being constructed around it . If 4/5 of the wall has been constructed , how much part of the wall is incomplete
Perimeter of the park = 10km
Part of the wall's construction completed =
[tex] \frac{4}{5}th \: of \: perimeter [/tex]
=
[tex] \frac{4}{5} \times 10[/tex]
(cancel 5 and 10)
=
[tex] \frac{4}{1} \times 2[/tex]
= 8km
•.• Part of the wall left (to be constructed) = 10km - 8km = 2km
HOPE THIS HELPS YOU
Derek has $80 to spend on used books. Hardcover books cost $10 each, and paperbacks cost $20 each. Complete the equation which determines the number x of hardcover books and the number y of paperback books he can buy.
A dealer sold 200 racquets. some were sold at rs 180 each and the rest at rs 330 each. the total receipts from these sales were rs 48000. how many racquests did the dealer sell at rs 180 each?
Answer:
120
Step-by-step explanation:
Number sold at rs180 = x
Number sold at rs330 = y
x + y = 200
180x + 330y = 48000
x = 200 - y
180(200 - y) + 330y = 48000
36000 - 180y + 330y = 48000
48000 - 36000 = 330y - 180y
12000 = 150y
12000/150 = y
y = 80
x = 200 - 80
x = 120
Some students equally share 2 baskets of apples.Each basket has 12 apples. Write an algebraic expression to represent this situation. Then explain how you chose which variable and operation to use.
The algebraic expression to represent the given situation is 24/x where x is the number of students.
According to the question,
We have the following information:
Some students equally share 2 baskets of apples. Each basket has 12 apples.
Now, this situation can be presented to find the number of apples each student had.
Let's take the number to students to be x.
(x is the variable in this case.)
Number of apples one student had = total number of apples/number of students
Number of apples one student had = (2*12)/x
Number of apples one student had = 24/x
Hence, the algebraic expression to represent the given situation is 24/x where x is the number of students.
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Tariq sold 2 kg, 4kg, 3 kg, and 4kg of almonds from Monday to
Thursday respectively. On Friday, he sold of the previous four days total
sold quantity.
a) How much almonds he sold on Friday?
b) How much almonds did he sell from Monday to Thursday?
Thi
a)
As per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:
a. Amount of almonds sold on Friday as per given condition is equal to
13 kg.
b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.
As given in the question,
Amount of almonds sold by Tariq from Monday to Thursday are as follow:
Monday = 2 kg
Tuesday = 4kg
Wednesday = 3 kg
Thursday = 4kg
a. Condition given:
Amount of almonds sold on Friday is equal to total sold quantity of previous four days that is Monday to Thursday
= (2 + 4 + 3 + 4) kg
= 13kg
b. Amount of almonds Tariq sell from Monday to Thursday is
= (2 + 4 + 3 + 4) kg
= 13kg
Therefore, as per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:
a. Amount of almonds sold on Friday as per given condition is equal to
13 kg.
b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.
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Company A offers to sell you the newest smart phone for $35.50 a month for one year or $35.50 per 1/12 of a phone. Company B offers the same phone on a two year plan at $18.00 a month or $18.00 per 1/24 of a phone. Which company is selling the phone for less money?
From the equations , the company A is selling the phone for less money
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equations for Company A :
The smart phone price per month = $ 35.50
The smart phone price for 1 year = $ 35.50 x 12
= $ 426
The price for 1/12 th of a phone = $ 35.50
The price for the entire phone = ( Price for 1/12 th of a phone ) x 12
= $ 35.50 x 12
= $ 426
Now , The equations for Company B :
The smart phone price per month = $ 18.00
The smart phone price for 2 year = $ 18.00 x 24
= $ 432
The price for 1/24 th of a phone = $ 18.00
The price for the entire phone = ( Price for 1/24 th of a phone ) x 24
= $ 432
Therefore , we can clearly see that price of the smart phone offered by Company A is lesser than price of the phone offered by Company B
And , $ 426 < $ 432
Hence , from the equations , the company A is selling the phone for less money
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PLEASE HELP QUESTION ON PICTURE!
Answer:
Exact answer 32[tex]\pi[/tex]
Estimate 100.48
Step-by-step explanation:
Circuference = [tex]\pi[/tex](diameter) Diameter is the distance across the cirlce going throught the middle
c = 32[tex]\pi[/tex]
Estimate
c = 3.14(32)
100.48
chart with the title 'average yearly earnings in the u.s. based on sex.' the blue line represents women's yearly average earnings. the red line represents men's yearly average earnings. the x-axis shows the years 1969, 1979, 1989, 1999, 2009, 2019. the y-axis shows the dollar amounts from 0 to 70,000 in increments of 10,000. in 1969, women earned 20,156 and men earned 32,241. in 1979, women earned 22,446 and men earned 37,622. in 1989, women earned 25,310 and men earned 36,855. in 1999, women earned 27,208 and men earned 37,701. in 2009, women earned 36,278 and men earned 47,127. in 2019, women earned 47,299 and men earned 57,456source: u.s. department of laborwhat is the relationship between the average yearly earnings of women and men? men continue to earn more than women. men work in higher skilled jobs where they earn more. women's earnings have increased in relation to men's earnings. women's earnings are lower because they take more time off.
The correct answer is Men continue to earn more than women.
The average yearly wages of men and women are different from one another. Men make more money than women do.
What is the annual salary?
Annual earnings may also be referred to as annual income or yearly income. It displays a person's earnings over a specific time period.
The yearly earning of a person or a corporation is calculated by dividing the monthly earnings by the number of months in a year.
Men continue to earn more than women under the situation mentioned above, hence their wages are higher. The red line is always above the blue line.
As a result, choice A is accurate which is men continue to earn more than women.
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Answer: C. women's earnings have increased in relation to men's earnings
Step-by-step explanation:
The chart shows that
a box of volume 252 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost.
The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
In the question ,
it is given that ,
the bottom of the box is = square ,
let the side of the square bottom be = "s" ,
so , the base area [tex]=[/tex] s²
let the height of the box [tex]=[/tex] h ,
Volume of the box = height × (base area)
So , the Volume of the box [tex]=[/tex] s²h
given that the volume of the box is 252 m³ , that means
s²h = 252
h = 252/s²
given that the Cost of bottom = $40 per m²
and the Cost of sides = $30 per m²
So , the total cost = 40s² + 30×(4sh)
substituting the value of h= 252/s² , we get
C = 40s² + 120s×252/s²
C = 40s² + 30240/s
to minimize the cost we differentiate with respect to s , and equating it to 0 ,
we get ,
80s - 30240/s² = 0
s³ = 30240/80
s³ = 378
s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it to 0 ,
we get ,
d²C/ds² = 80 + (30240*2)/s³
at s=7.23 , d²C/ds² > 0
So , the minimum is at s = 7.23 ,
we have h = 252/(7.23)²
h = 4.82 .
Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m .
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A farmer determined the equation "y = -7/3x + 72.75" best fits his data when comparing the weight, y, in grams, of strawberries to the average daily mean temperature, x, in °F, each season. Which statement best describes the rate of change of the equation?
(Save me its mental abuse)
The rate of change, -7/3, in the equation means: the average weight of strawberry decrease by 7/3 grams at every 1°F increase in temperature.
How to Interpret the Rate of Change of an Equation?A linear equation is often expressed in the form of y = mx + b, which is the slope-intercept form, where the rate of change is the value of the variable "m" in the equation, and b is the starting or initial value.
Given the equation, y = -7/3x + 72.75, in slope-intercept form, where:
y = weight in grams of strawberries x = average daily mean temperatureTherefore:
-7/3 in the equation represents the rate of change.
72.75 represents the starting value or y-intercept.
The rate of change, -7/3, in the context of this situation as represented in the equation can be described as: 7/3 grams average weight that is decayed at every 1°F increase in temperature.
Therefore, the statement that best describes the rate of change is: There is 7/3 grams decrease in weight of the strawberry at every 1°F increase in temperature.
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True or false: The associative property is used on the following expression: 2 + 3 = 3 + 2.
if its false what is the answer
Answer: I believe this is True!
Step-by-step explanation:
I know what associative property and that seems like a example.
And if its false then answer should be false.
Try True, if not True then False!
What is 78=13n sovle for n
Answer:
Step-by-step explanation:
13n=78 /13
n= 6
find the tension in each string and the acceleration of the 3-box system below if there is no friction
Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
In 3 - box system:
There are two tensions and two strings, let T1 and T2 be the tensions.
Let mass of boxes be m1,m2,m3
total mass m = m1+m2+m3
Acceleration a = force / m
a = f/m1+m2+m3
T1 = m2 * f/m
T2 = m3 * f/m.
Therefore Tension in each string in the 3 - box system is T1 = m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.
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If you invest $200 into a savings account that earns 4% annual interest compounded continuously, how much money will you have after 21 years?
Answer:
$455.75
Step-by-step explanation:
Formula for compound interest:End amount = Starting amount x (1 + interest in decimal form)^length of time in years Starting amount: $200Interest rate as a decimal: 0.04 (4%/100)Length of time: 21 yearsEnd amount = 200.00(1 + 0.04)^(21) = $455.75
(1 point) a cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 7.5. what are the dimensions of such a cylinder which has maximum volume?
For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
As given in the question,
Height of the right circular cone = 2.5 units
And radius of right circular cone = 7.5 units
Let r be the radius of the cylinder and h be the height of the cylinder.
Volume of a cylinder 'V' = π r² h
Cylinder is inscribed in right circular cone
From origin edge cylinder is inscribed at x distance in right circular cone.
r = 7.5 - x
h = (2.5 /7.5) x
= x/3
V = π ( 7.5 - x )² ( x / 3)
⇒ V = π ( x² -15x + 56.25 ) (x/3)
⇒ V = (π /3)( x³ - 15x² + 56.25x)
For maximum volume ,
dV/dx = 0
dV/dx = (π/3)( 3x² -30x + 56.25)
(π/3) ≠ 0
⇒ 3x² -30x + 56.25 = 0
⇒ 3 ( x² -10x + 18.75) = 0
3 ≠ 0
⇒ x² -10x + 18.75 = 0
x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)
⇒ x = [ 10 ± √ 100 -75]/2
⇒ x= ( 10 ± 5 ) / 2
⇒ x = 7.5 or 2.5
As r = 7.5 -x
Hence x ≠ 7.5
r = 7.5 -2.5
= 5 units
h = x/3
= 2.5/3
= 0.8333 units
Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
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Your bank account has -$30, and you deposit $7 daily. How much money is your account after 5 days? Show you work with the Unit!
16 points
The amount in the account after the daily deposit for 5 days is $5
How to determine the amount in the account?The given parameters i the question are represented as follows
Initial balance = -$30
Daily deposit = $7
Number of days of deposit = 5
The equation that represents the amount in the account is represented as
Amount = Initial balance + Daily deposit * Number of days
Substitute the known values in the above equation So, we have the following equation
Amount = -30 + 7 * 5
Evaluate
Amount = 5
Hence, the amount is $5
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Slope
=
1
2
y-intercept = 0
Answer:
[tex]y=\frac{1}{2}x[/tex]
Step-by-step explanation:
I don’t know exact what is being asked but I got this
slope intercept form is y=mx+b
m=slope
b=y intercept
[tex]y=\frac{1}{2}x+0[/tex]
[tex]y=\frac{1}{2}x[/tex]
Hopes this helps please mark brainliest
The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere. (The center of the earth is also the center of the equator.) What is the length of the equator? (numerical answer only; no units)
The length of the equator is 40192 km.
How to find the length of the equator?The radius of the earth is approximately 6400 km. The equator is the circle around the earth dividing it into the northern and southern hemisphere.
Let's find the length of the equator as follows:
The length of the equator is the circumference.
Therefore,
L = 2πr
where
r = radiusL = 2 × 3.14 × 6400
L = 6.28 × 6400
L = 40192 km
Therefore, the equator which is the circle around the earth has a length of 40192 km.
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Find the slope (3,0),(-11,-15)
Answer: 15/14
Step-by-step explanation:
Use the slope formula: y2-y1/x2-x1
Apply that:
-15-0/-11-3 = -15/-14 = 15/14