The commission rate is 44.8%.
What is the commission rate?The first step is to determine the commission on the first $10,000 : 0.1 x 10,000 = 1,000
The second step is to determine the commission on the next $15,000: 0.12 x $15,000 = $1,800
The third step to determine the commission on amounts more than $25,000 : x%(29,665 - 25,000)
x%(4,665)
Total commissions earned on amount more than $25,000 : $4,891 - (1,800 + 1,000) = $2091
Now, determine the commission rate : $2091 / $4,665 = 0.448 = 44.8%
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You're going on a 1211-mile trip, and your car gets about 29 miles per gallon. Gas prices along your route average $3.10. Estimate the cost of gasoline for this trip by rounding the distance to 1200 miles, the mileage to 30 miles per gallon, and the cost of gas to $3.00 per gallon. Calculate the answer without using estimation and compare the two results. (Round your answers to the nearest cent.)
Using proportions, it is found that:
Without estimation, the cost is of $129.46.With estimation, the cost is of $120.For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Without the estimate, the number of gallons used is:
1211/29 = 41.76 gallons.
Hence the cost is:
41.76 x 3.10 = $129.46.
With the estimate, the number of gallons used is:
1200/30 = 40 gallons.
Hence the cost is:
40 x 3 = $120.
For the estimation, the mileage was rounded up while the cost was rounded down, hence the estimated cost is less than the actual cost.
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how to factorise 3x + 6
Answer:
it is 3(x+2)
Answer:
3(x+2)
Step-by-step explanation:
You first find the common factor.
3x+6
3(x+2) solution.
A naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet then 145 is the position of the submarine relative to the surface of the ocean now.
What is Equation?
Two expressions with an equal sign is called as Equation.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet. we need to find the position of the submarine relative to the surface of the ocean now.
The submarine initial position=310 feet.
To pass above an underwater mountain, or seamount, it rose =165 feet.
The position of submarine is
310-165
=145 feet.
Therefore the position of the submarine relative to the surface of the ocean now is 145 feet.
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can someone help me with this
The cost per passenger for no wind conditions is $199 and 33 cents
Ground speed, 'x' = 500 ± 0 = 500 miles/h;
Cost per passenger is given by;
C(x) = 100 + x/15 + 33000/x;
Put x = 500;
C(500 miles/h) = 100 + 500/15 + 33000/500
C(500 miles/h) = $199.33
The cost per passenger for no wind conditions = $199 and 33 cents;
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What is the answer at the A - B i don't know how to do this so I want answer or explanations The
Answer:
where is the question bro?
Step-by-step explanation:
If a// b and m 1 = 90° then m 2 =
Slope m2=90°
The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.
given that, since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
so we can conclude since m1=90° the m2 is also = 90°
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Answer:
M2 slope = 90°
Step-by-step explanation:
The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.
Given that parallel lines must have the same angle from the horizontal and that slope is a measurement of that angle, parallel lines must therefore have the same slope, therefore lines with the same slope are parallel.
We can then deduce that if m1=90°, m2 must also be 90°.
Write the equation of the line with slope 35 that passes through point (0,−3).
Answer:
[tex]y = 35x - 3[/tex]
Step-by-step explanation:
Based on the given conditions
[tex]m = 35[/tex]
Substitute and calculate
Substitute:
[tex]m = 35 \\ x = 0 \\ y = - 3[/tex]
Into:
[tex]y = mx + b[/tex]
Therefore, the equation of the line is:
[tex]y = 35x - 3[/tex]
A restaurant has 11 2/5 pounds of pasta to make casserole dishes. Each casserole requires 2 2/3 pounds pasta. How many casseroles can be made?
Answer:
Step-by-step explanation:
4.275
112/5 / 22/3
What is the difference between adjusting entries and correcting entries? explain
Answer:
In short, the difference between adjusting entries and correcting entries is that adjusting entries bring financial statements into compliance with accounting frameworks, while correcting entries fix mistakes in accounting entries.
Which type of compound inequality is 3|y+7|-16>5
-union
-hole
-disjunction
-intersection
y < -14ory > 0
Rearrange variables to the left side of the equation: 3|y+7| >5+16
Calculate the sum or difference: 3 |y+7| >21
Divide both sides of the inequality by the coefficient of the variable: |y+7| >[tex]\frac{21}{3}[/tex]
Reduce the fraction: |y+7|>7
Convert the absolute inequality to standard inequality: y+7 >7ory +7 < -7
:y < -14ory > 0
Find the union: y < -14ory > 0
A variable in mathematics is a sign and placeholder for any mathematical object (from the Latin variabilis, "changeable"). A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.
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Select the correct answer form each drop-down menu.
Given: m/WOZ = 90°
Prove: m/WOX = 90°
X
W
N
Complete the proof.
Suppose m/WOX # 90°. By the
✓ZWOXis supplementary to ZWOZ. Therefore,
m/WOX + m/WOZ = 180°. By the assumption and the substitution property of equality. 90° +m/WOZ 180°. Using the
subtraction property of equality, the measure of angle WOZ
✓90°, which contradicts the given. Therefore, the
assumption is not true, and m/WOX = 90°.
4
Reset
Next. Answer?
The complete proof are;
Suppose m ∠WOX ≠ 90°. By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore, m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given.
Therefore, the assumption is not true and m ∠WOX = 90°.
What are Supplementary angles?
The two angles are called supplementary angles when sum of both angles are 180 degree.
Given that;
m ∠WOZ = 90°
Now, The proof of m ∠WOX = 90° is given as;
Suppose m ∠WOX ≠ 90°.
By the definition of linear pair of straight line ∠ WOX is supplementary to ∠WOZ.
Therefore,
⇒ m ∠WOX + m ∠WOZ = 180°.
By the assumption and the substitution property of equality.
⇒ 90° + m ∠WOZ = 180°.
Using the subtraction property of equality, the measure of angle WOZ is equal to 90°, which contradicts the given assumption.
Therefore, The assumption is not true and m ∠WOX = 90°.
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write three rations equivalent to 3/10
Answer:
6/20, 9/30, 12/40
Step-by-step explanation:
Original fraction: 3/10
How I got: 6/20
3 x 2 = 6
10 x 2 = 20
How I got: 9/30
3 x 3 = 9
10 x 3 = 30
How I got: 12/40
3 x 4 = 12
10 x 4 = 40
Find the difference between the largest and the smallest of the four numbers below.
10,743.93
234.018
324.1
23.107
Answer:
10720.823
Step-by-step explanation:
largest number is 10743.93 and the smallest number is 23.107. subtracting 23.107 from 10773.93 to get 10743.93
Is 4:6 and 8:12 equivalent to each other
Answer:
YES!
Step-by-step explanation:
ratios are like fractions, and fractions are basically division problems. SO, if you divide 4 by 6 you get .66666666, and if you divide 8 by 12 you ALSO get .66666666, soooooo yes they are equivalent!
Find the sum of 2.53 x 1019 and 3.197 x 1017.
2.56197 x 1019
3.2223 x 1019
2.56197 x 1036
3.2223 x 1036
Taking into account the scientific notation, the result of the sum is 2.56197×10¹⁹.
Scientific notationScientific notation is a quick way to represent a number using powers of base ten.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.Sum in scientific notationYou want to add the following two numbers in scientific notation:
2.53×10¹⁹3.197×10¹⁷When the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 19.
Then all the values are expressed as a function of the base 10 exponent with the highest exponent. In this case: 3.197×10¹⁷= 0.03197×10¹⁹
Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:
2.53×10¹⁹ + 0.03197×10¹⁹= (2.53 + 0.03197)×10¹⁹= 2.56197×10¹⁹
Finally, the result of the sum is 2.56197×10¹⁹.
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How do I graph -2x + 6 < 4 and 3(x + 1) < 12 on a number line?
Step-by-step explanation:
u first have to simplify a bit so u expand giving u -2x+6 less than 4 u then group like terms giving u -2x less than 4-6 amounting to -2x less than-2 u then divide both side by negative two to make x stand alone giving u positive 1 when u get Yr answer because u divided by a negative answer the sign changes to greater than
53
4. Consider the rational number and the irrational number √78.
6
(a) Use your calculator to write out the (b) Which number is greater? Justify.
decimal expansion for both. If necessary,
use the repeating decimal bar.
53
6
√√78=
Difference between mixed farming and mixed cropping
El área total de la superficie de un cilindro circular recto es 196 centímetros cuadrados. Si el radio de la base y la altura del cilindro tienen la misma longitud, encuentre la longitud de un radio.
--
The total surface area of a right circular cylinder is 196
The length of the radius when the total surface area of a right circular cylinder is 196 cm² is 7√π cm.
How to illustrate the information?It should be noted that the total surface area will be calculated thus,:
= 2πr(h + r)
It was stated that the radius and the.lebgth are the same and that the area is 196. This will be:
2πr(r + r)
= 2πr(2r)
= 4πr²
Therefore, 4πr² = 196
πr² = 198/4
πr² = 49
πr² = 49
r² = 49/π
r = 7√π
Therefore, the length of the radius when the total surface area of a right circular cylinder is 196 cm² is 7√π cm.
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A plane climbs from an altitude of 6000 ft to a cruising altitude of 39,000 ft. The plane ascends at a rate of 6600 ft/min. How long will it take to reach cruising altitude?
The time taken to ascend from the initial height to the final height; Time taken = 5 minutes
What is the time taken?We are given;
Initial Height = 6000 ft
Final height = 6600 ft/min
Speed = 6600 ft/min
Now, the time taken to ascend from the initial height to the final height;
Time taken = (39000 - 6000)/6600
Time taken = 5 minutes
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Sixty-one percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?
The unusual outcomes for the binomial distribution are given as follows:
0 or 1 employee making judgements.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the binomial distribution, a measure is considered unusual if it is more than 2.5 standard deviations from the mean.
For this problem, the parameters are given as follows:
n = 8, p = 0.61.
Hence the mean and the standard deviation are given by:
E(X) = np = 8 x 0.61 = 4.88.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8(0.61)(0.39)} = 1.38[/tex]The bounds of usual outcomes are:
4.88 - 2.5 x 1.38 = 1.43.4.88 + 2.5 x 1.38 = 8.33.Hence outcomes of less than 1 employee making judgements would be unusual.
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 40 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of
degrees.
The measure of the largest angle is 84°
How to compute the value?It should be noted that the total angles on a triangle is 180°.
Let the smallest angle = x
Second angle = x + 40
Third angle = 3x
Therefore 3x + x + x + 40 = 180
5x = 180 - 40
5x = 140
x = 140/5
x = 28
Therefore, the largest angle will be:
= 3x
= 3 × 28°
= 84°
Therefore, the measure of the largest angle is 84°
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HELP WITH NUMBER 5 FOR 20 POINTS
Answer:
5
Step-by-step explanation:
that is hte anwers
Bo kept track of his cookie sales. He
discovered that 3 out of 5 people who
came into his bakery for cookies bought
chocolate chip cookies.
If 400 customers bought cookies at Bo's
Bakery last month, how many of them
bought chocolate chip cookies?
Answer:240
Step-by-step explanation:
400/5 = 80
80 x 3 = 240
240/400 people bought choc chip
2. Consider the graph of y = f(x) below.
YA
F
14
/2 -1 0
-1+
+
1 2
(a) Find all values for which f(x) is discontinuous.
(b) For each point in (a), describe where the 3-part definition fails.
(c) Classify each discontinuity as jump, removable, or infinite.
Answer:
Step-by-step explanation:
31
Solve the equation
2^2x+1 + 2^x+2 = 12-2^x
Therefore the value of x is 2.
Given 2²ˣ ⁺ ¹ + 2ˣ ⁺ ² = 12 * 2ˣ
2²ˣ ⁺ ¹ + 2ˣ ⁺ ² = 12 * 2ˣ
We can write this as follows
aˣ ⁺ ⁿ = aˣ * aⁿ
2²ˣ * 2 + 2ˣ * 2² = 12 * 2ˣ
2ˣ * 2ˣ * 2 + 2ˣ * 2² = 12 * 2ˣ
By taking common terms aside we get
2ˣ * 2 (2ˣ + 2) = 12 * 2ˣ
By canceling the like terms we get
2ˣ + 2 = 6
2ˣ = 6 - 2
2ˣ = 4
2ˣ = 2²
∴ x = 2
Therefore the value of x is 2.
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Convert the following ratios into percentages.
2:3
Answer:
66%
Step-by-step explanation:
Answer:
66 %
Step-by-step explanation:
It is 66 % because to convert you have to follow these steps
Step 1: Identify the ratio.
Step 2: Express the ratio a:b in the form of a fraction a/b.
Step 3: Multiply the fraction by 100.
Step 4: Simplify and write the answer with the percent symbol (%).
Question 5 (1 point)
Match the expressions that are equivalent.
Column A
1/32
32
2
1/2
64
1/64
Column B
a. (2^3)(2^2)
b. 2^(-2) x 2^(-3)
C. (2^3) x (2^-3)
d. (2^2)^3
e. 2^2/2^3
f. 2^3/2^2
It should be noted that the correct matching of the expressions illustrated will be:
a. (2^3)(2^2) = 32
b. 2^(-2) x 2^(-3) = 1/32
C. (2^3) x (2^-3) = 1
d. (2^2)^3 = 64
e. 2^2/2^3 = 1/2
f. 2^3/2^2 = 2
How to illustrate the information?It should be noted that (2^3)(2^2) will be:
= 2³ × 2²
= 8 × 4
= 32
b. 2^(-2) x 2^(-3) will be illustrated as:
= 1/4 × 1/8
= 1/32
C. (2^3) x (2^-3)
= 8 × 1/8
= 1
d. (2^2)^3
= 4³
= 64
e. 2^2/2^3
= 4 / 8
= 1/2
f. 2^3/2^2
= 2³ / 2²
= 8 / 4
= 2
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Find x for this equation
Show clear algebraic fraction
Answer:
x = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5x-2}[/tex] = [tex]\frac{3}{6x+1}[/tex] ( cross- multiply )
3(5x - 2) = (2(6x + 1) ← distribute parenthesis on both sides )
15x - 6 = 12x + 2 ( subtract 12x from both sides )
3x - 6 = 2 ( add 6 to both sides )
3x = 8 ( divide both sides by 3 )
x = [tex]\frac{8}{3}[/tex]
PLS HELP!! 25 POINTS + BRAINLIEST
Answer:
A. 5/4n - 3/8
Step-by-step explanation:
-5n/2 + 1/4 + 15/4n - 5/8
15/4n - 10/4n + 2/8 - 5/8
5/4n - 3/8
A party planner purchased roses to decorate tables for an event. There were 15 tables and 5 roses were placed on each table. If the roses were $1.98 each, how much did the party planner spend on roses?
A. $148.50
B. $29.70
C. $9.90
D. $75.00
Answer: 148.50
Step-by-step explanation:
15*5=75
75*$1.98=$148.50
