Answer:
Step-by-step explanation:
Let's assume that the first car used x gallons of gas during the week, then the second car used (75 - x) gallons of gas because the total gas consumption by both cars is 75 gallons.
The first car's fuel efficiency is 30 miles per gallon, so it traveled (30x) miles during the week.
The second car's fuel efficiency is 35 miles per gallon, so it traveled (35(75 - x)) miles during the week.
The total distance traveled by both cars is given as 2425 miles, so we can set up the equation:
30x + 35(75 - x) = 2425
Expanding the equation:
30x + 2625 - 35x = 2425
Simplifying:
-5x = -200
x = 40
Therefore, the first car used 40 gallons of gas during the week, and the second car used (75 - 40) = 35 gallons of gas during the week.
Answer: Car 1 used 40 gallons and car 2 used 35 gallons.
Step-by-step explanation: In this problem, we will use a system of equations to reach our answer. We can let x be the gallons consumed by the first car, and y be the gallons consumed by the second car(these are both for one particular week only). We know the total consumption of gas is 75 gallons so the gallons consumed by car 1 and car 2 have to add up to 75. We can then create the equation x+y=75. We know that car 1 has an efficiency of 30 miles per gallon and 35 miles per gallon for car 2. The miles produced by x gallons in car 1 can be represented by 30x=# of miles. we can use 35y = # of miles for car 2. We know the combined total of miles from both cars is 2425 so we can make the equation 30x+35y=2425 miles. Now that we have our equations, we can simply solve them to find our answers.
x+y=75
x=75-y Isolating a variable
30x+35y=2425
30(75-y)+35y=2425 Substituting the variable we isolated
2250-30y+35y=2425
2250+5y=2425
5y=175
y=35
x+(35)=75
x=40
y=35 and x=40
Car 1 used 40 gallons and car 2 used 35 gallons.
Hope this helps!
dibuja una línea desde cada ecuación hasta la propiedad de igualdad que ilustra
Answer:
Lo siento, como modelo de lenguaje de IA, no tengo la capacidad de visualizar o dibujar gráficos. ¿Puedo ayudarte con algo más?
f(t)= 5-2t is the answer -39.1%
Yeah, your right the answer would be -39.1%
Pls help asap rewarding Brainliest
Im not fully sure but it might be the 3rd one!
. A survey was conducted to determine the types of occupations of the 1,200
residents of a town. The types of occupations are shown in the circle graph.
Occupations
Retail
25%
Education
15%
Industry
25%
Other
30%
Government
Based on the circle graph, how many more residents have an occupation in
industry than have an occupation in government?
A.360
B.300
C.240
D. 20
240 more residents have an occupation in industry than have an occupation in government. The solution has been obtained by using arithmetic operations.
It is believed that the four fundamental operations, often referred to as "arithmetic operations", can describe all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are divide, multiply, add, and subtract.
We are given a graph determining the types of occupations of the 1,200 residents of a town.
Percentage of residents having occupation in government is:
100% - 25% - 15% - 25% - 30% = 5%
Number of residents having occupation in industry is as follows:
25% of 1200 = 300
Similarly, number of residents having occupation in government is:
5% of 1200 = 60
Number of more residents that have occupation in industry than have an occupation in government is:
300 - 60 = 240
Hence, 240 more residents have an occupation in industry than have an occupation in government.
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The circle graph was missing in the question which has been attached below.
if 9% of a number equals 10 find 27% of that number
Answer:
30
Step-by-step explanation:
You divide the number so 10 by 9 giving you the 1% of it and then you times that number by 27 to get 27%.
Answer:
30
Step-by-step explanation:
9%*3=27%
10*3=30
or more simply what you do to one you have to do to the other.
Can you describe this transformation?
The transformation is a reflection over the x-axis.
What is the transformation applied?
On the given graph we can see two triangles, one is pointing up and the other one is pointing down, from that we clearly can see that we hade a kind of reflection.
Now, the distance between the base of the top triangle and the x-axis is 4 units.
The distance between the top side of the bottom triangle and the x-axis is aslo 4 units.
Then the reflection is over the x-axis.
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Look at this table.
Gallons Cost, in
of Gas Dollars
1 2.15
2 4.30
4 8.60
10 21.50
? 30.10
20 43.00
What value is missing from the table?
A. 15
B. 14
C. 16
D. 13
please help me with trigonometry
The length of the guy wire to the nearest foot would be = 10 ft.
How to calculate the length of the guy wire?The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.
The distance from the stake to the pole (opposite) =a = 5 ft
The distance from the pole to the tower (adjacent) =b= 9ft
The length of the guy wire= c = X
Using the Pythagorean formula:
c² = a² + b²
c² = 5² + 9²
c² = 25+81
c² = 106
C = √106
C= 10 ft ( to the nearest foot)
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Complete question:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.
y= 4x^(3/2)+x^(1/2)
Find the differential of the function.
dy=
The differential of the function is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
How to find the differential of the function.From the question, we have the following parameters that can be used in our computation:
y= 4x^(3/2)+x^(1/2)
Using the first principle of differentiation, we have
dy/dy = 3/2 * 4x^(3/2 - 1) + 1/2 * x^(1/2 - 2)
Evaluate the expressions
dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
Hence, the solution is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
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WILL GIVE BRAINLIEST
(Theoretical Probability MC)
Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
List 1 List 2 List 3 List 4
O
0,0 0,0 0,0
G
O, GO, GO, G
B
O, B O, BO, B
G, O G, OG, O
G, B
G, B
G, B
G, G
G, G
G, G
B, B
B, BB, B
B, GB, GB, G
B, O B, O
G, O
O, B
G, B
Which list gives the sample space for pulling 2 marbles from the bag with replacement?
List 1
List 2
List 3
List 4
Here are the possible outcomes of randomly drawing two marbles from the bag:
O, G
O, B
G, O
G, B
B, O
B, G
There are six possible outcomes in total, each with an equal chance of occurring. Therefore, the theoretical probability of drawing an orange marble and a green marble from the bag is 1/6 or approximately 0.167.
The number of trout in a stocked lake is given by the
equation T = 1800 (1.15)n where n is the number of months since the start of the trout season.
a. How many trout will there be in 2.5 months?
b. How many trout were there 2 months before the season opened?
a. To find the number of trout in 2.5 months, we can substitute n = 2.5 into the given equation:
T = 1800 (1.15)^n
T = 1800 (1.15)^2.5
T ≈ 2708.67
Therefore, there will be approximately 2,709 trout in the lake after 2.5 months.
b. To find the number of trout 2 months before the season opened, we need to use a negative value of n that represents the time before the start of the trout season. If we assume that the start of the season is month 0, then 2 months before the start of the season would be month -2. Thus, we can substitute n = -2 into the given equation:
T = 1800 (1.15)^n
T = 1800 (1.15)^(-2)
T ≈ 980.92
Therefore, there were approximately 981 trout in the lake 2 months before the start of the trout season.
I need help finding what the indicated IQ score is. This is my elementary statistics homework question
The IQ score given the mean and the standard deviation, can be found to be 105. 25.
How to find the IQ score ?To find the indicated IQ score corresponding to a right tail area of 0.3694, we can use a standard normal distribution table or calculator. Using a calculator, we can find that the z-score corresponding to a right tail area of 0.3694 is approximately 0.35.
Once we have the z-score, we can use the formula z = (x - μ) / σ to solve for the IQ score :
0.35 = (x - 100) / 15
Solving for x, we get:
x = 0.35 x 15 + 100
= 105.25
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Write a unit rate for the situation.
3600 stitches in 3 minutes
Answer:Hence, there are 1200 1200 1200 stiches per minute.
Step-by-step explanation:
The cost of one burrito b, and one taco a is less than the cost of two burritos. Which
inequality represents this relationship?
b+a<2b
b+a
b+a> 2b
b + a ≤ 2b
Answer:
The inequality that represents this relationship is:
b + a < 2b
Determine whether the study is an experiment or an observational study, and then identify a major problem with the study.
In a survey, 1465 Internet users chose to respond to this question posted on a newspaper's electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes."
Question content area bottom
Part 1
This is an
▼
experiment
observational study
because the researchers
▼
do not attempt to modify
apply a treatment to
the individuals.
Part 2
What is a major problem with the study?
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
B.
There is no blinding or replication, which has a high chance of leading to bias.
C.
The sample is not very large.
D.
The results apply only to Internet users
The study is classified as an observational study, and the problem is given as follows:
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
What are experiments and observational studies?Experiments are studies in which there are two groups, with different features, and then the effect of a feature is studied.
For an observational study, there are no changes, just a question is asked, as is the case for this problem.
Convenience samples lead to bias as many people that share characteristics can answer.
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What is the vertical asymptote and horizontal asymptote pic attached below
The required horizontal and vertical asymptote is x = 2, -2, and y = 1/4.
How to find Asymptotes?To find the vertical asymptotes of the given rational function, we need to look for values of x that make the denominator zero, since division by zero is undefined.
The denominator of the function is 4(x-2)(x+2), so the vertical asymptotes occur at x = 2 and x = -2. Therefore, the vertical asymptotes are:
x = 2, -2
To find the horizontal asymptote, we can use the fact that as x goes to positive or negative infinity, the function approaches the ratio of the leading coefficients of the numerator and denominator.
In this case, the leading term in the numerator is x² and the leading term in the denominator is 4x². Therefore, as x approaches positive or negative infinity, the function approaches:
y = (x² / 4x²) = 1/4
So, the horizontal asymptote is:
y = 1/4
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
[tex]f(x) = x^{2} -5x + 12[/tex]
The graph of the function is a parabola → true
____
The value of f(–10) = 82 → false[tex]f(-10) = (-10)^{2} -5(-10) + 12 = 100+50+12 = 162 \neq 82\\[/tex]
The graph of the function opens down → false The graph contains the point (20, –8) → false[tex]f(20) = (20)^{2} -5(20) + 12 = 400-100+12 = 312 \neq - 8\\[/tex]
The graph contains the point (0, 0) → false[tex]f(0) = 0^{2} -5(0) + 12 = 0 - 0 + 12 = 12 \neq 0\\[/tex]
Need help on solving this math problem!!
Answer:Hello!-47 s the answer :)
Step-by-step explanation:
Need help ASAP
the value of each variable. If your answer is not
teger, express it in simplest radical form.
The length of a is
The length of b is
(Simplify your answer.)
Answer:
me too (help)
Step-by-step explanation:
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
Step-by-step explanation:
its 1
Find the slope of the line passing through each of the following pairs of points (-6,-5) (-4,-3)
The Slope of the line is 1.
The slope of a line:The slope of a line is a numerical value that shows the stiffness or direction of the line. The formula used to find the Slope of the line is given by
Slope (m) = [ y₂ - y₁] / [ x₂ - x₁]Where (x₁, y₁) and (x₂, y₂) are pairs of points that pass through the line.
Here we have
The pair of points (-6, -5) and (-4, -3)
By using the formula,
The slope of the line = [ y₂ - y₁] / [ x₂ - x₁]
= [ -3 - (-5) ] / [ -4 - (-6) ]
= [ -3 + 5 ]/ [ -4 + 6 ]
= [ 2/2] = 1
Therefore
The Slope of the line is 1.
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How do I solve this and what’s the answer?
he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13
The standard deviations of the data are different.
Standard deviation:
The formula used to calculate the standard deviation of data is given by
Standard deviation = √[ ∑(x[tex]_{i}[/tex] - x)² /n ]x - mean of the data and n = number of observations
Here we have
(a) 4, 5, 11, 13, 13, 14
Mean of the data = [4 + 5 + 11 + 13 + 13 + 14 ]/6 = 60/6 = 10
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 96
=> √[ ∑(x[tex]_{i}[/tex] - x)²/n ] = √[ 96/ 6 ] = 4
(b) 5, 7, 10, 10, 13, 15
Since the mean of the data is equal for all
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 68
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 68/ 6 ] = 3.36
(c) 3, 10, 11, 11, 12, 13
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 64
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 64/ 6 ] = 3.26
Therefore,
The standard deviations of the data are different.
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Need help with number 90
Answer:
a = 16.5
b = 8.8
Step-by-step explanation:
How far away from his was Liam after 15 minutes?
The requried, Liam is 24 blocks away from his house.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
A graph is shown, Liam left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Liam is x minutes after he left his house until he got back home.
In order to calculate Liam's distance after x = 15 minutes. Draw a perpendicular at x = 15 that intersects the curve. Since the line intersects the curve at y = 24. This implies that Liam is 24 blocks away from his house.
Thus, the requried Liam is 24 blocks away form his house.
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Which graph represents the solution to the inequality 0.5 is greater than or equal to the product of a number and −0.25?
A. number line with closed circle on 0.5 with arrow shaded right
B. number line with open circle on point on negative 0.5 with arrow shaded left
C. number line with closed circle on negative 2 with arrow shaded right
D. number line with open circle on 2 with arrow shaded left
Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
What is inequality?
An inequality is a comparison relationship between two or more mathematical expressions.
We are given an inequality as 0.5 is greater than or equal to the product of a number and −0.25.
Let the number be x.
So, from the above information, we get the inequality as
0.5 ≥ -0.25x
Now, on solving the above inequality, we get the following
0.5 ≥ -0.25x
On multiplying by -1, we get
⇒-0.5 ≤ 0.25x
On dividing both sides by 0.25, we get
⇒-2 < x
Hence, Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
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find the code find the quotient write your answer using a decimal and round to the nearest hundredth 8,426 / 82
Answer:The quotient of 8,426 divided by 82 can be found using long division or a calculator. When rounded to the nearest hundredth, the quotient is:
102.85
Therefore, the answer is 102.85.
Step-by-step explanation:
2 Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same.
Tom's total annual tax for the following year, assuming the tax table remains the same, is R325,287.17.
How much tax will Tom pay per year?To calculate Tom's tax for the following year, we need to first calculate his current monthly PAYE (Pay As You Earn) deduction. We can use the current tax table to do this.
Tom's gross salary is R25,780.25 per month, and he is 45 years old, so according to the 2021/2022 tax table for individuals under 65 years old, his monthly PAYE deduction is:
= R1,458.75 + 25% of the amount over R14,958
= R4,569.96
Tom argues that his PAYE will increase by R593.09 for the following year. This means that his expected monthly PAYE deduction for the following year is:
= R4,569.96 + R593.09
= R5,163.05
Tom's salary for the following year will increase by 8.5%, so his new gross salary will be:
= R25,780.25 + (8.5% x R25,780.25)
= R27,959.83
Tom's pension fund contribution remains the same at 7.5% of his gross salary:
= R27,959.83 x 7.5%
= R2,097.49
His charity organization contribution increases by R50.00 per month:
= R50.00 x 12
= R600.00
Assuming the tax table remains the same as the previous year, Tom's new monthly PAYE deduction is:
= R1,577.98 + 26% of the amount over R17,708
= R5,502.86
To calculate Tom's total annual tax, we need to subtract his annual PAYE deduction from his gross salary and then add back his pension and charity contributions:
Total annual tax = (R27,959.83 x 12) - (R5,502.86 x 12) + R2,097.49 + R600.00
Total annual tax = R325,287.17.
Full question "Tom is 45 years old. He earns a gross salary of R25,780.25 per month.. Tom argues that his PAYE for the following year will increase by R593.09. The following year Tom's salary increases by 8.5%. How much tax will Tom pay per year, if he still contributes only 7.5% of his gross salary to a pension fund but increases his contribution to the charity organization by further R50.00 a month? Calculate as if the tax table for the following year remains the same."
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What is 2^-2 equal to?
A. -4
B. -1/16
C. 1/4
D. 1/2
Answer:
best of my knowledge hope its right -4
Step-by-step explanation:
if S is 150% of T, then T is what percent of S+T
The percentage representation of T as part of S + T as required is; 40 percent.
What is the percentage representation of T as part of S + T?As evident in the task content;
S is 150% of T.
S = 150/100 × T
S = 1.5T.
Therefore, expressing T as a percentage of S + T as required is as follows;
= (T / (S + T)) × 100%
substitute S = 1.5T into the equation
= T / (T + 1.5T) × 100%
= (1/2.5) × 100%
= 0.4 × 100%
= 40%.
Ultimately, the variable T is 40 percent of S + T.
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