If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill
The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%
The amount of tax = The price of the grocery bill before tax × (7.3/100)
Substitute the values in the equation
= 265.24 × (7.3/100)
= 265.24 × 0.073
= $19.36
The final bill including tax = The price of the grocery bill before tax + The amount of tax
Substitute the values in the equation
= 265.24 + 19.36
= $284.6
Therefore, the grocery bill including tax = $284.6
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3. Apply Math Models Cynthia earns $680 in
commissions and is paid $10.25 per hour. Javier
earns $410 in commissions and is paid $12.50 per
hour. What will you find if you solve for x in the
equation 10.25x + 680 = 12.5x +410?
The earnings for both Cynthia and Javier are same for x hours.
What is commission?
When an employee completes a task, typically selling a certain volume of goods or services, they are compensated financially. Sales commissions are occasionally used by employers as incentives to boost employee productivity. It is possible to receive a commission in place of or in addition to a salary.
Given:
Cynthia earns $680 in commissions and is paid $10.25 per hour.
Javier earns $410 in commissions and is paid $12.50 per hour.
So, the equation is
10.25x + 680 = 12.5x + 410
To simplify this equation for x.
10.25x+ 680 =12.5x +410
680 ‐ 410 = 12.5x ‐ 10.25x
270 = 2.25x
x = 270/2.25
x = 120
If we plug x = 120 in both the values 10.25x + 680 and 12.5x + 410 then we will get the same values.
Hence, the earnings for both Cynthia and Javier are same for x hours.
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Write at least four more addition or multiplication equations for 2 in which all
the fractions have a denominator of 8.
Answer:
Step-by-step explanation:
2 + 3/8 = 7/8
2 x 7/8 = 7/4
2 + 5/8 = 9/8
2 x 9/8 = 9/4
2 + 6/8 = 8/8
2 x 8/8 = 16/8
2 + 7/8 = 15/8
2 x 15/8 = 15/4
Are the lines A and B parallel? (The figure may not be drawn to scale). Please help!! Giving brainliest for whoever has the right answer
Answer:
Yes, they are parallel.
Step-by-step explanation:
61 + 119 = 180
One line is 180 degrees.
Gabe is the human resources manager for the Advanced Scientific Research Lab. He has to record the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab. Height distribution (cm) 178 163 174 186 154 167 167 181 159 165 177 191 158 Weight distribution (lbs) 157 163 190 187 183 173 184 189 193 192 177 173 168 13 Select the correct answer. What is the shape of the height and weight distribution? A. The height and weight distribution exhibit a negative and a positive skew, respectively. B. Both the height and weight distribution exhibit a positive skew. C. Both the height and weight distribution exhibit a negative skew. D. Both the height and weight distribution are symmetric about the mean. E. The height and weight distribution exhibit a positive and a negative skew, respectively.
Last option: The height and weight distributions, respectively, show positive and negative skews.
What is bar graph?Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.
There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.
[tex]\frac{change}{strating point } X 100%[/tex]
2.5 millions of books were sold in 1991.
Millions of books sold in 1992 equaled 3.4.
Change = 0.9 (in millions).
[tex]\frac{0.9}{2.5} X 100 = 36[/tex]%
The height and weight distributions, respectively, show positive and negative skews.
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Which of these represents the graph of x + 3y = 6
Answer:
PLEASE ADD A DANG PICTURE
Step-by-step explanation:
What is an equation of the line that passes through the point ( 2 , − 3 ) (2,−3) and is perpendicular to the line 2 x + 5 y = 10 2x+5y=10?
Answer: y=-[tex]\frac{5}{2}[/tex]x+2 or 5x+2y=4
Step-by-step explanation:
let’s make l1: 2x+5y=10,
then 5y=-2x+10
then y=-[tex]\frac{2}{5}[/tex]x+2
So k1=-[tex]\frac{2}{5}[/tex]let’s make the unknown line equals l2: y=k2*x + bBecause l2 is perpendicular to l1, so k2*k1=-1then who can calculate k2=-[tex]\frac{5}{2}[/tex]Because l2 passes the point (2,-3),so when x=2, we can know y=-3we can get an equation is -3=-[tex]\frac{5}{2}[/tex]*2 +bSo b=2l2: y=-[tex]\frac{5}{2}[/tex]x +2 or 5x+2y=4A company's minimum cost of $1000 occurs when operating for 16 hours per day. The cost of operating 8 hours per day would be $2600. Write a quadratic equation that models the company's costs.
The quadratic equation that models the company's costs is y = 25(x - 16)² + 1000
How to determine the quadratic equation that models the company's costs.From the question, we have the following parameters that can be used in our computation:
Minimum cost of $1000 at 16 hours
Operating cost of $2600 at 8 hours
A quadratic equation is represented as
y = a(x - h)² + k
The minimum point is the vertex
So, we have
(h, k) = (16, 1000)
Substitute (h, k) = (16, 1000) in y = a(x - h)² + k
y = a(x - 16)² + 1000
The cost of $2600 at 8 hours means
(x, y) = (8, 2600)
So, we have
2600 = a(8 - 16)² + 1000
Evaluate the difference
1600 = a(8 - 16)²
So, we have
64a = 1600
Divide by 64
a = 25
Substitute a = 25 in y = a(x - 16)² + 1000
y = 25(x - 16)² + 1000
Hence, the equation is y = 25(x - 16)² + 1000
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Is this a function? Explain, why or why not!
Answer:
No
Step-by-step explanation:
A function can have only output for each input. The input 3 has two outputs 3 and 5.
The input 4 has two outputs 4 and 6.
in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time. group of answer choices true false
in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time is a True statement.
In a simple linear regression equation, the independent variable is the one that is used to predict the dependent variable. In this case, time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.A linear regression equation is used to describe the relationship between two variables, where one is the independent variable and the other is the dependent variable. The independent variable is the one that is used to predict the dependent variable. In this case, time series data is being used to forecast the trend in sales, so time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.
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2. Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Day 1:
Day 2:
Comparison of Day 1 and Day 2: _-4___ ___5____
Comparison of days with absolute value: __ _______
Inequalities are used to compare unequal expressions.
The actual comparison is: -3.5F < 5F or 5F > -3.5F
Given,
In the question:
Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Now, According to the question:
The temperatures are given as:
Temperature: -3.5F, 5F, 1.5F, -0.5F, -2F, 2.5F, -4F
From the above list, we have:
Day 1 : -3.5F
Day 2 :- 5F
By comparison,
-3.5F < 5F or 5F > -3.5F
Using absolute values, the inequalities are:
|-3.5F| < |5F| or |5F| > |-3.5F|
Hence, the actual comparison is:
-3.5F < 5F or 5F > -3.5F
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $264.00. On her second business trip she drove 200 miles in 3 days, and paid $165.00 for the rental. Find the daily fee, and find the mileage charge.
A specialty shop procures several grandfather clocks for $200 apiece and offers them to customers
or $568 each. What percentage is the mark-up?
Use the picture equation
what is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2. statement (1) alone..
For the given statement about hundredth digit of the given decimal z the following statement is true:
Option E. statement (1) and (2) together are not sufficient.
As given in the question,
Let us consider decimal z is represented by k.lmn
Here hundredth digit of z is equal to m
Now,
(1) The tenths digit of 100z is 2.
100z
= 100(k.lmn)
=klm.n
This implies n = 2
(2) The units digit of 1,000z is 2.
1,000z
= 1,000(k.lmn)
= klmn
This implies n =2
From both the statements we are getting the value of n which is not sufficient to get the value of required 'm'.
Therefore, Option E is the correct answer which shows both the statements are not sufficient to get the value required hundredth digit of decimal z.
The complete question is:
What is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.
A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.
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the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams. what is the probability that the next report will weigh less than 45 grams?
The probability that the next report will weigh less than 45 grams = 0.106
In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.
We need to find the probability that the next report will weigh less than 45 grams.
We have mean= 60 grams
Standard Deviation = 12 grams
First we convert 45 to z score.
45 converted to z score for given mean and standard deviation will be:
z = (45 - 60)/12
z = -1.25
So, from standard normal table a P-value:
P(x<45) = 0.10565
Therefore, the probability would be 0.10565
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Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
Given that:
The area of rectangular room is 750 square feet.
Let the length of the rectangular room be y feet.
Since the width of the rectangular 5 less than the length of the room.
Then the width of the given rectangular room is (y-5) feet.
We know the area of a rectangular plot is = Length×width.
Thus , the area of the rectangular room is = y(y-5) square feet
According to problem,
area of the rectangular room = 750 square feet
⇒ y(y-5) =750.........(1)
⇒ y²-5y=750 .......(2)
⇒ y²-5y-750=0
⇒ y²-30y+25y-750=0
⇒ y(y-30)+25(y-30)=0
⇒ (y-30)(y+25)=0 ......(3)
⇒ y-30=0 or, y+25=0
⇒ y= 30, -25
∵ the length of a rectangle can't be negative.
So, y=30.
We can rewrite the equation (1) in form of
(i)
y(y-5) =750
⇒750= y(y-5)
⇒750-y(y-5)=0.......(4)
(ii)
y(y-5) =750
⇒y(y-5) -750=0.......(5)
Hence , the equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
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Please answer quickly
1) The length of AC is 14.
2) The length of AB is 8.
3) The length of BC is 17.
4) The length of AB is 29.1.
5) The length of BC 53.
6) The measure m∠C is 53.8°
What is sine rule of a triangle?
AB/sin C = BC/ sin A = AC / sin B
1)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
22° + 118° + ∠C = 180°
∠C = 40°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 24, ∠C = 40°, and ∠B = 22°:
AB/sinC=AC/sin B
24/sin 40° = AC/ sin 22°
AC = 13.98
AC ≈ 14
2)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 7, ∠B = 44°, and ∠C = 53°:
AC/sin B=AB/sin C
7/sin 44° = AB/ sin 53°
AB = 8.047
AC ≈ 8
3)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
39° + ∠B + 51°= 180°
∠B = 90°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 27, ∠B = 90°, and ∠A = 39°:
BC/sinA=AC/sin B
BC/sin 39° = 27/ sin 90°
BC = 16.99
BC ≈ 17
4)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
∠A + 101° + 63°= 180°
∠A = 16°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting CB = 9, ∠A = 16°, and ∠C = 63°:
AB/sinC=BC/sinA
AB/sin 63° = 9/ sin 16°
AB = 29.09
AB ≈ 29.1
5)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
93° + ∠B + 58° = 180°
∠B = 29°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 16, ∠B = 29°, and ∠A = 93°:
AC/sinB=BC/sin A
16/sin 29° = BC/ sin 93°
BC = 32.95
BC ≈ 33
6)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 21, ∠A = 88°, and BC= 26:
AB/sinC=BC/sinA
21/sin C = 26/ sin 88°
sin C/21 = sin 88°/26
C = 53.82
C ≈ 53.8
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Use the information in the table f (x), the graph g (x)and equation h (x) to evaluate the following expressions.
Drag and drop the most appropriate answer in the box provided.
Question 1
[tex](f \circ g)(-2)=f(-2) \cdot g(-2)=10 \cdot 3=\boxed{30}[/tex]
Question 2
[tex](g \circ h)(1)=g(1) \cdot h(1)=2(1^2 -9)=\boxed{-16}[/tex]
Question 3
[tex](g/f)(0)=\frac{g(0)}{f(0)}=\frac{0^2 -9}{6}=\boxed{-3/2}[/tex]
Question 4
[tex](h/f)(-3)=\frac{h(-3)}{f(-3)}=\frac{3^2 -9}{12}=\boxed{0}[/tex]
Add 3[tex]\frac{5}{6}[/tex]+(-1[tex]\frac{1}{6}[/tex] Write your answer as a mixed number in simplest form.
Answer: 2 2/3 or 8/3
Step-by-step explanation:
3 5/6 = 23/6
-1 1/6 = -7/6
23/6-7/6
16/6
simplify
8/3
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
3 [tex]\frac{5}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex] = [tex]\frac{23}{6}[/tex] ( [tex]\frac{6}{6}[/tex] is the same one)
1 [tex]\frac{1}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex]
Adding a negative number is like subtracting a positive number.
[tex]\frac{23}{6}[/tex] - [tex]\frac{7 }{6}[/tex] = [tex]\frac{16}{6}[/tex] 6 goes into 16 2 times with 4 left over
2 [tex]\frac{4}{6}[/tex] Divide the top and bottom by 2 to get
2 [tex]\frac{2}{3}[/tex]
There are more than 360 different breed of dog recognized worldwide. Which inequality repreent thi tatement?
x > 360
x < 360
x ≥ 360
x ≤ 360
Answer:
should be the first one, x > 360
Step-by-step explanation:
im sorry if its wrong :*(
I'm stuck I need help :(
(5x+1)(3x-5)-(x-3)(5x+1)
Answer:
is 2(x minus 1)(5x + 1)
Step-by-step explanation:
Please help find the value of x!!
Answer:31
Step-by-step explanation: solve it
Which relation is also a function?
Answer:
Step-by-step explanation:
I am not 100% positive but I am 75% positive it is B.
13 Which situation could be modeled by a linear function?
(1) The value of a car depreciates by 7% annually.
(2) A gym charges a $50 initial fee and then $30 monthly.
(3) The number of bacteria in a lab doubles weekly.
(4) The amount of money in a bank account increases by 0.1%
monthly.
The situation could be modeled by a linear function is
(2) A gym charges a $50 initial fee and then $30 monthly.
What is a linear function?A linear function in mathematics is one that has either one or two variables and no exponents.
2) Let y be the total amount charged by the gym to a person for x months.
as the initial amount for every person is $30.
The gym charges [tex]50+30x[/tex] $ after x months.
Hence this is a linear equation.
The remaining situations cannot be expressed as a linear equation because they include percentages in them.
Every situation that has a percentage is an exponential function.
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How long is the hypotenuse of a right triangle 24 square inches in area and with one leg 6 inches long? A. 24 inches B. 18 inches C. 12 inches D. 10 inches
Answer:
D
Step-by-step explanation:
area of triangle = 1/2*B*H
Assuming its one leg we write
24 = 1/2*6*h
h= 8
With this info we can use Pythagoras Theorum
[tex]a^{2} = b^{2} + c^{2}[/tex]
[tex]x^{2} = 8^{2} + 6^{2}[/tex]
[tex]x^{2} = 100[/tex]
[tex]\sqrt{100}[/tex]
[tex]x = 10[/tex]
Write the linear equation of the following graph in slope-intercept form.
y =-1/2x
y=1/2x
y=-2x
y=2x
please help!!!!
The linear equation of the following graph in slope-intercept form will be; y=1/2x
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The slope of the line is calculated as follows:
m = Δy/Δx
To find the linear equation of the following graph in slope-intercept form.
Therefore, the slope of the line is;
m = Δy/Δx
m = 1/2
When we simplify it, then we get the equation as;
y=1/2x
Hence, The linear equation of the following graph in slope-intercept form will be; y=1/2x
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Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x. What does 47.3 mean in the context of the problem?
Responses
A For every inch of rain that falls 47.3 bushels of wheat are produced .For every inch of rain that falls 47.3 bushels of wheat are produced.
B If no bushels of wheat were produced, 47.3 inches of rain fell.If no bushels of wheat were produced, 47.3 inches of rain fell.
C For every bushel of wheat that is produced, 47.3 inches of rain fell.For every bushel of wheat that is produced, 47.3 inches of rain fell.
D If no rain fell, 47.3 bushels of wheat would be produced.
The thing that 47.3 mean in the context of the problem is D. If no rain fell, 47.3 bushels of wheat would be produced.
What does 47.3 mean in the context of the problem?It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x.
It should be noted that when no rain fell, 47.3 bushels of wheat would be produced. This is the constant value.
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Please Help Me ASAP!!!!!!!!!
Answer: 6,3
Step-by-step explanation:
Answer:
6,3
Step-by-step explanation:
A fair spinner has 12 equal sections: 3 red, 5 blue and 4 green.
It is spun twice.
What is the probability of getting not green then green?
Answer:
2/9 = approximately 0.22.
Step-by-step explanation:
There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.
To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.
Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.
Could Someone Help Me with this rewrite dis equation into y=mx+b
y< -3/4x+2
The equation in the form of y=mx+b will be y= -3/4x+2
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that the inequality is y< -3/4x+2,
We have to write the inequality in the form of y=mx+b
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the equation in the form of y=mx+b will be y= -3/4x+2
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