The state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.
We are given that:
The rate of tax on sales for South Salt Lake is = 7.05 %
That is:
Sale tax rate = r = 7.05 %
Now, we are given that the selling price of a car = $ 21,900
Selling price = $ 21,900
Now we need to find the sales tax amount that will be imposed on the car.
For this, we will calculate the percentage.
Sales tax = 7.05 % of $ 21,900
Sales tax = 7.05 % × $ 21,900
Sales tax = 7.05 / 100 × $ 21,900
Sales tax = 7.05 × $ 219
Sales tax = $ 1543.95
Therefore, we get that the state sales tax on a car of $ 21,900 in South Salt Lake will be $ 1543.95.
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he graph represents the heights of two climbers on a climbing wall over a 12-minute time period.
A graph where the horizontal axis shows time (minutes), numbered 1 to 12, and the vertical axis shows height (feet) numbered 2 to 24. The line labeled Brynn's climb begins at 0 feet in 0 minutes, to 15 feet from 5 to 7 minutes, to 0 feet in 10 minutes. The line labeled Abby's climb begins at 4 feet in 0 minutes, to 14 feet from 4 to 6 minutes, to 22 feet in 8 minutes, to 0 feet in 12 minutes.
How high did Abby climb above her original starting position?
8 feet
15 feet
18 feet
22 feet
Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and.
Review Andrew’s work, identify the error and correct all work from that point forward that is affected by this error. Include at least one sentence explaining his error. Use proper mathematical vocabulary, appropriately.
The supplied roots' polynomial equation is x³-7x²+20x-24=0.
A polynomial equation is defined as:A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree. To be a polynomial equation, the variable in the equation must contain only non-negative integer exponents. Specifically, variable exponents should be non-negative and neither negative nor fractional.
According to the given data:Given that, solution polynomial equation of the least degree has roots of 3, 2+2i, and 2-2i.
Now, x=3, x=2+2i and x=2-2i
x-3, x-2-2i and x-2+2i
So, the polynomial equation is (x-3)(x-2-2i)(x-2+2i)=0
=(x-3)(x(x-2-2i)-2(x-2-2i)+2i(x-2-2i))=0
=(x-3)(x²-2x-2xi-2x+4+4i+2xi-4i-4i²)=0
=(x-3)(x²-2x-2x+4-4i²)=0
=(x-3)(x²-4x+4+4)=0 (∵i²=-1)
=(x-3)(x²-4x+8)=0
=x(x²-4x+8)-3(x²-4x+8)=0
=x³-4x²+8x-3x²+12x-24=0
= x³-7x²+20x-24=0
The supplied roots' polynomial equation is x³-7x²+20x-24=0.
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If Isabelle went on a slide that was 100 feet long with a ladder to the
top measuring 35 feet, how far is the bottom of the slide to the bottom
of the ladder? Round to the nearest foot.
93.7 feet is the distance from the bottom of the slide to the bottom of the ladder.
Let us consider the distance from the bottom of the ladder to the bottom of the slide "x" (the unknown we want to find).
The ladder's length is 35 feet, and the slide's length is 100 feet.
According to the Pythagorean theorem:
c² = a² + b²
where c is the hypotenuse (the ladder's length), and a and b are the two other sides of the right-angled triangle (the distances we want to find).
In this case, the equation becomes:
35²= x² + 100²
Solving for x:
1225 = x² + 10000
x² = 10000 - 1225
x² = 8775
Taking the square root of both sides to find "x":
x = √8775
x = 93.7 feet
So, the distance from the bottom of the slide to the bottom of the ladder is 93.7 feet.
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If the ladder slipped so that the foot was 2 m from the wall, how far down the wall did the ladder slip?
Answer:
e foot
Step-by-step explanation:
Answer:
How far down the wall did
the ladder
Step-by-step explanation:
A sporting goods factory puts 500 playground balls in each shipment. How many playground balls will there be in 5 shipments?
Answer:
100
Step-by-step explanation:
Find the distance from point X to line p.
The distance from point X to line p is 2√17 units.
We are given the point X as:
X = ( - 2 , 5 )
We need to find the distance of X from the line p.
We will do this by using the distance formula:
Distance = √ (y₂ - y₁)² + (x₂ - x₁)²
Distance = √ (- 2 - 0) ² - (5 - ( - 3)) ²
= √ ( - 2) ² - (5 + 3) ²
= √ ( - 2) ² - (8) ²
= √ 4 + 64
= √ 68
= 2 √17 units
Therefore, the distance from point X to line p is 2√17 units.
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Your question was incomplete. Please find the content below:
Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:
A. 2 √34 units
B. √85 units
C. 2 √17 units
D. √17 units
Suppose a meteorologist is tracking rainfall patterns in Mickton, Florida. Select all true statements.
Mickton had more rainy days in June 2012 than November 2012, December 2012, and January 2012 combined.
There was only one month with more rainy days in 2013 than 2012.
Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013.
There were 13 rainy days in February 2013.
The month with the greatest difference in the number of rainy days between 2012 and 2013 was December.
The correct statements regarding the given bar graph are as follows:
Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013.There were 13 rainy days in February 2013.The month with the greatest difference in the number of rainy days between 2012 and 2013 was December.What does a bar graph show?A bar graph shows the number of times that each observation appears in the data-set.
The first correct statement is:
Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013.
As:
30 + 29 > 8 + 5 + 11 + 7 + 10 + 4
The second correct statement is:
There were 13 rainy days in February 2013.
Due to the blue bar in Feb.
The third correct statement is:
The month with the greatest difference in the number of rainy days between 2012 and 2013 was December.
Difference of 10 - 4 = 6 days, which is the biggest.
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Perform the indicated computation and express the answer in decimal notation.
(4x10 to the power of 4) (2x10 to the power of 3) =
The indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000
How to perform the indicated computation and express the answer in decimal notation?The expression is given as
(4x10 to the power of 4) (2x10 to the power of 3) =
Rewrite properly, as:
(4 x 10^4) (2 x 10^3) =
Evaluate the product of 4 and 2
So, we have
(4 x 10^4) (2 x 10^3) = 8 x 10^4 x 10^3
Evaluate the product of 10^4 and 10^3 using the law of indices
So, we have
(4 x 10^4) (2 x 10^3) = 8 x 10^7
Evaluate the product of 8 and 10^7
So, we have
(4 x 10^4) (2 x 10^3) = 80000000
Hence, the indicated computation of (4 x 10^4) (2 x 10^3) in decimal notation is 80000000
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i dont now how to do this
Answer:if they choose the family tickets its 15% off the regular ticketts individually
Step-by-step explanation:
can someone help me really quick
Answer:
ain't no way you need help my bou
What is the equation of the line?
y = 3/4 x + 1
y = 4/3 x − 1
y = 4/3 x + 1
y=3/4x−1
Answer: 15
Step-by-step explanation:
Question 5
▼ <
>
A company makes a profit when it brings in more money than it pays out. The company only has enough
resources to make 8500 items in a quarter. Suppose a company's revenue in a quarter (the amount brought
in) can be modeled by R 195x, and its costs per quarter (the amount paid out) can be modeled by
C 160x+18000, where a is the number of items sold. How many items must be sold for the
-
=
company to make a profit?
The number of items that must be sold for the company to make a profit is 757.
Calulation of number of items sold:
R = 195x
C = 160x + 18000
Here R means the revenue
And, C means the cost
Now
We know that
Profit = R - C
Profit = Revenue - cost
=195x - (160x + 18000)
= 195x - 160x - 18000
= 35x -18000
Now solve the above equation
So,
35x - 18000 = 8500
x=757
Therefore,
x = 757
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8 + 3 4 ÷ -2 3 = what?
-10
By BODMAS Method
8 + 3*4 ÷ -2*3
8 + 3* [tex]\frac{4}{-2}[/tex] *3
8 + 3*-2*3
8 +(-18)
-10
The order of operations (BODMAS) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression.
For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.
As a result, 1 + (2 × 3) = 7, rather than (1 + 2) × 3 = 9. is the value assigned to the expression 1 + 2 × 3. BODMAS was first used in the 16th and 17th centuries when addition and multiplication were given priority. BODMAS could only is used as a superscript to the right of their base.
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6. The genetic information of almost
every living thing is stored in a tiny
strand called DNA. Human DNA is
3.4 x 10-8 meter long.
a. Write the length in standard form.
b. How many significant
digits are there in the
measurement?
The la
The length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters
Also, the significant figure in the measurement = 1
In this question, we have been given the length of human DNA.
The genetic information of almost every living thing is stored in a tiny strand called DNA.
Human DNA is 3.4 x 10-8 meter long.
We need to write the length in standard form.
3.4 x 10-8 meter
= 3.4 x 10 ^ (-8)
= 3.4 x 0.00000001
= 0.000000034
= 0.00000003
Here Significant Figures = 1
Decimals = 8
And the length in Scientific Notation = 34[tex]e^{-8}[/tex] meters
Therefore, the length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters
Also, the significant figure in the measurement = 1
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Відповідь: 1)
5. Розв'яжіть систему рівнянь способом підстановки
2)
3y = 10,
5х + y = 2.
-
Answer:
Step-by-step explanation:
x - 3y = 10
5x + y = 2
x - 3y = 10
15x + 3y = 6
16x = 16
x = 1
5 + y = 2
y = -3
(1, -3)
HELLO i’ll give BRAINLIEST TO THE PERSON WHO ANSWERS!!!
From the numeric value of the formula, the tuition and fees for the school year ending in 2010 was of $26,270.
How to find the numeric value of a function?The numeric value of a function is found replacing each instance of x by the value that we want to find.
For this problem, the cost function is given by:
T(x) = 26x² + 806x + 15610.
In which x is the number of years after 2000.
Hence the cost in 2010 will be given by:
T(10) = 26(10)² + 806(10) + 15610 = $26,270.
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Solve for b.
2²376.
b+5=20-b
b=
Answer: b=7.5
Step-by-step explanation:
b+5=20-b
b+b+5=20-b+b ==> add b on both sides to put b on only one side of the equation
2b+5=20
2b=15
b=7.5
Given the rule what is the new coordinate?
the image (new coordinate) after the translation is (-2.5, 9.8)
How to find the new coordinate by using the given rule?
Here we have a rule (also called a transformation or an operator) that works as:
T(x, y) = (x - 7.5, y + 6.8)
So we decrease the x-value by 7.5 and increase the y-value by 6.8. This is a translation of 7.5 units to the left and 6.8 units upwards.
Now, our point is (5, 3), if we apply that transformation we will get:
T(5, 3) = (5 - 7.5, 3 + 6.8) = (-2.5, 9.8)
That is the image after the translation.
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Pls help me with both of these
The algebraic expression for the phrase "the quotient of y and 6" is y / 6
The difference of -3 - 4 is -7.
How to solve algebraic expression?The algebraic expression of the following phrase "the quotient of y and 6" is as follows:
Quotient is a quantity produced by the division of two numbers.
Therefore, the algebraic expression for the phrase "the quotient of y and 6" is y / 6
The difference of -3 - 4 can be calculated as follows:
The difference of -3 - 4 is -7.
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Please answer this question for me. Urgent.
Using a system of equations, the expression, in terms of x, for the total number of students at the college is:
T = 11x.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem
For this problem, considering the Venn diagram, we have that:
A + x students play the Piano.B + x students play the Guitar.Thus the total number of students in the college is given by:
T = A + B + x.
1/2 of the students who learn the piano also learn the guitar, hence:
A = x.
Thus the number of students who play the piano is:
A + x = x + x = 2x.
5 times as many students learn the guitar as learn the piano, hence:
B + x = 5(2x)
B + x = 10x
B = 9x.
Hence:
T = A + B + x
T = x + 9x + x
T = 11x.
The expression, in terms of x, for the total number of students at the college is:
T = 11x.
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Which of the following is a false statement?
A
Banks are insured by the government.
B
Money can be stolen or lost if you keep it at home.
C
If your bank goes out of business, you lose your money.
D
Your money can grow if you keep it in a bank account.
C ) If your bank goes out of business, you lose your money is a false statement .
Since banks are insured by FDIC . So if a bank becomes dissolves or becomes bankrupt FDIC covers the loss of customers of bank upto a certain limit .
A ) Banks are insured by the government.
This is a true statement .
B ) Money can be stolen or lost if you keep it at home . Even this is a true statement .
D ) Your money can grow if you keep it in a bank account . This is also a true statement .
Hence , C ) If your bank goes out of business, you lose your money is a false statement .
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The end points of ab are A (-7,3) and B (1,0) find the coordinates of the midpoint M
Answer:
(-3,3/2)
Step-by-step explanation:
It's easy just add the abscissa and ordinate individually and divide the obtained abscissa and ordinate by 2
|||
=
Knowledge Check
In the figure below, j Il n. Find the values of y and z.
شکر
60°
y4z-20)
Question 5
A
11
Z =
0
Answer:
y=120
z=20
Step-by-step explanation:
angle below y is 60° because of corresponding angles
y=180-60=120
y+(4z-20)=180(angles in a straight line)
120+4z-20=180
100+4z=180
4z=180-100
4z=80
z=80/4
z=20°
2x-y + 2z = -6
-3y +z = -2
2x-3z=4
Enter your answer, in the form (z, y, z), in the boxes in simplest terms
{x, y, z} = { -16/13, -10/13, -28/13}.
What is the value of BC.
Answer:
BC = 13
Step-by-step explanation:
x + 10 + x + 14 = 22
2x + 24 = 22
2x = -2
x = -1
BC = x + 14 = -1 + 14 = 13
A satellite flies 114550 miles in 22.91 hours. how many miles has it flown in 6.97 hours?
If a satellite flies 114550 miles in 22.91 hours, then it will flies 34850 miles in 6.97 hours
Given,
The total distance flies by the satellite = 114550 miles
Time taken = 22.91 hours
Speed of the satellite = Distance / Time taken
[tex]\frac{114550}{22.91} =5000[/tex] miles per hour
The total distance flown by the satellite in 6.97 hours
Distance = Speed × Time
= 5000×6.97
=34850 miles
Hence, if a satellite flies 114550 miles in 22.91 hours, then it will fly 34850 miles in 6.97 hours
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HELP URGENT!! the data set for a random sample of 10 soccer players heights compared to their shoe sizes is summarized in the table.
questions included in the photo.
Part A: The equation of least squares regression line is
ŷ = 0.4684X + 64.69888
Part B: The residual that we have here is - 1.382
Part C: Residual refers to the difference between the observed value and the predicted value
How to solve for the residualSum of X = 102.5
Sum of Y = 695
Mean X = 10.25
Mean Y = 69.5
Sum of squares (SSX) = 33.625
Sum of products (SP) = 15.75
Regression Equation = ŷ = bX + a
b = SP/SSX = 15.75/33.63 = 0.4684
a = MY - bMX = 69.5 - (0.47*10.25) = 64.69888
ŷ = 0.4684X + 64.69888
Residual = observed - predicted
The observed = 68
The predicted = 0.4684 x 10 + 64.69888
= 4.684 + 64.69888
= 69.382
residual = 68 - 69.382
= -1.38
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sa finished 30% of his homework in 27 minutes. How many more minutes will it take Isa to complete his homework, assuming that he works at the same pace?
A. 63 minutes
B. 67 minutes
C. 70 minutes
D. 90 minutes
Answer:D
Step-by-step explanation:
Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday. How many total hours did he work last weekend?
If Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours
How to solve for the number of hoursThe total numbers of hours that was worked can be solved by
7 11/12 hours * 84%
= 95 / 12 * 84 / 100
= 7980 /1200
= 6.65
Therefore we can say that if Brandon works at the waterpark on the weekends. Last Saturday, he worked 7 11/12 hours. On Sunday, he worked 84% of the hours he worked on Saturday, The total hours that he would have to work on the weekend is 6.65 hours
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Answer:
6 hours and 39 minutes is the correct answer.
Step-by-step explanation:
So, set up your problem...
STEP 1: 84% out of 100%, or 84/100
STEP 2: 7 11/12 is a mixed number, so to make solving easier, make it an improper fraction: 95/12
- 7 11/12
- 7 × 12 = 84 + 11 = 95
- Keep the denominator (12)
- 95/12 is now an improper fraction.
STEP 3: Multiply 95/12 × 84/100 = 6.65
STEP 4: Convert to hours...
- Note that 6.65 hours and 6:65 is not the same. 6.65 hours with the decimal point is 6.65 hours in terms of hours. 6:65 with the colon is 6 hours and 65 minutes.
- Start by dividing up what is before and after the decimal point. 6 = hours, .65 = fractional hours
- To convert from 6.65 decimal hours to hours and minutes, we need to convert the .65 fractional hours to minutes.
- Since there are 60 minutes in an hour, you multiply the .65 fractional hours by 60 to get minutes. .65 × 60 = 39 minutes.
So, in conclusion, the correct answer to your question is... 6 hours and 39 minutes.
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What postulate proves triangle congruence?
*
25 points
Captionless Image
AAS
SAS
SSS
ASA
The postulate that proves that the triangles are congruent is: SAS congruence postulate.
How to Apply the Side-angle-side Congruence Postulate (SAS)?The SAS congruence postulate states that when two triangles have a pair of included congruent angles, and two pairs of corresponding sides that are congruent, then both triangles are congruent.
In the triangles given, we have:
Two pairs of corresponding sides that are congruent - BL ≅ PF and BG ≅ PX
A pair of included congruent angles - <B ≅ <P.
This means both triangles are congruent by SAS.
Therefore, the postulate that proves that the triangles are congruent is: SAS congruence postulate.
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