Simplify the expression.
x^3/2/x^1/2
[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}=x^{\frac{3}{2}-\frac{1}{2}}=x^{\frac{3-1}{2}}=x^{\frac{2}{2}}=x^1=x\\\\Answer:\ \boxed{x}[/tex]
The spoke of wheel reaches from the center of the wheel to its rim if the circumstance of the wheel is 48 inches, how long is each spoke? Use 3.14 for and round your answer to the nearest hundredth.
Answer:
7.6 in
Step-by-step explanation:
c = 2πr Divide each side by 2π
r = C/2π Insert values
r = 48/(2×3.14)
r = 48/6.28
r = 7.6 in
Karla can buy guppies for $0.90 each at the corner pet store. If she has $13.50, how many guppies can she buy?
All we have to do here is divide $13.50 by $0.90 to figure out how many guppies she can buy
$13.50 ÷ $0.90 = 15
Therefore, Karla can buy 15 guppies with $13.50
Hope this helps you
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- AaronWiseIsBae
Rachel is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 5 sizes, 2 flavors, and 1 topping to choose from. How many different ice cream desserts could she order?
To calculate the different ice cream desserts Rachel can order, we use the formula for combinations without repetition. Given 5 sizes, 2 flavors, and 1 topping, the number of choices for each category: 5 sizes x 2 flavors x 1 topping = 10 different ice cream desserts Rachel could order.
Total ice cream desserts = (Number of sizes) × (Number of flavors) × (Number of toppings)
= 5 × 2 × 1
= 10
So, Rachel could order 10 different ice cream desserts by combining the choices for size, flavor, and topping.
If Petrol cost 1.20 per gallon how much would 5 3/4 cost?
Answer:
Step-by-step explanation:
1.20 x 5.75
=$6.90
The cost of petrol is given per gallon. Therefore, to find the cost of 5 3/4 gallons of petrol, multiply the cost per gallon which is 1.20 by the number of gallons, 5 3/4, that gives 6.90. Hence, 5 3/4 gallons of petrol would cost 6.90.
Explanation:To find out the cost of 5 3/4 gallons of petrol, we first need to understand that the cost is listed per gallon. This means that for every gallon, you pay 1.20. So, to calculate the cost of 5 3/4 gallons, we just need to multiply the cost per gallon by the number of gallons.
So, the cost of 5 3/4 gallons would be: 1.20 (cost per gallon) x 5 3/4 (number of gallons) = 6.90.
Therefore, 5 3/4 gallons of petrol would cost 6.90.
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What is the midpoint between z1 = -8 + 3i and z2 = 4 + 7i?
Answer:
Therefore, Mid point : -2+5i.
Step-by-step explanation:
Given : Z1 = -8 + 3i and Z2 = 4 + 7i.
To find : What is the midpoint.
Solution : We have given Z1 = -8 + 3i and Z2 = 4 + 7i.
Mid point : [tex]\frac{z_{1}+z_{2}}{2}[/tex].
On plugging the values.
Mid point : [tex]\frac{-8+3i + 4 +7i}{2}[/tex].
Combine like terms.
Mid point : [tex]\frac{-8+4+3i +7i}{2}[/tex].
Mid point : [tex]\frac{-4+10i}{2}[/tex].
Mid point : -2+5i.
Therefore, Mid point : -2+5i.
125 is 500% of what number
let's say that number is "x", so "x" is then the 100%.
we know 125 is the 500%, and "x" is the 100, what is "x"?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 125&500 \end{array}\implies \cfrac{x}{125}=\cfrac{100}{500}\implies \cfrac{x}{125}=\cfrac{1}{5} \\\\\\ 5x=125\implies x=\cfrac{125}{5}\implies x=25[/tex]
2700=300•2^10x solve for x
A population of bacteria increases by 30 every hour. Is this situation linear or exponential? A. Exponential, because the function grows by a common factor B. Exponential, because the function decreases C. Linear, because the function decreases D. Linear, because the function increases by a constant amount
Answer:
The correct option is D.
Step-by-step explanation:
In a linear function the rate of change is constant. It means either the function increase by a constant rate or function decrease by a constant rate.
In an exponential function the rate of change is not constant.
It is given that the population of bacteria increases by 30 every hour.
Since the population of bacteria increases by a constant rate therefore the population function is linear and it is defined as
[tex]P(t)=P_0+30t[/tex]
Where P₀ is initial population and t is time in hours.
Therefore correct option is D.
In the situation where a population of bacteria increases by a constant amount every hour, the growth pattern is linear, not exponential. Exponential growth in bacteria involves a doubling (or increase by a certain factor), not a fixed increase, and results in a J-shaped curve when plotted over time.
Explanation:The situation presented in the question, where a population of bacteria increases by 30 every hour, represents a linear function. This is because the function increases by a constant amount. So, the answer is D. Linear, because the function increases by a constant amount. The given scenario differs from an example of exponential growth typically seen in bacteria. In exponential growth, the population of bacteria would double (or increase by a certain factor) each hour as opposed to increasing by a fixed amount. Exponential growth in bacteria occurs when there is an unlimited supply of nutrients, and the population size, when plotted over time, results in a J-shaped growth curve. Here, the rate of increase itself increases with time. In contrast, the linear growth described in the question indicates a steady rate of increase.
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Solve using elimination
5x+3y=24
-2x-7y=-56
Answer:
Solution point (0,8)
Step-by-step explanation:
Multiply the top equation by 2
2*(5x + 3y = 24) Remove the brackets10x + 6y = 48 You could simplify this but don't.And multiply the bottom equation by 55*(-2x - 7y = -56)-10x - 35y = -280Now add the two equations together.
10x + 6y = 48 -10x -35y = - 280 The xs cancel out-29y = - 232 Divide by - 29y = -232/-29 Do the division y = 8=================
Solve for x
5x + 3y = 24 Substitute for y5x + 3*8 = 24 Combine on the left5x + 24 = 24 Subtract 24 from both sides 5x = 0 Divide by 5x = 0==================
This one is just a bit messier. I made a graph of it just to show that the answer is correct.
A sporting good store is offering an additional 30% off all clearance items and she purchases a pair of running shoes on clearance for $65 if the shoes originally cost $85 what was her total discount?
Answer:
Total discount = $39.50
or 46.47 %
Step-by-step explanation:
First we need to figure out what she will pay for the shoes. She is getting 30 percent off the 65 dollars.
Discount = price * percent off
= 65*.3
= 19.50
The cost of her shoes is the price minus the discount.
Cost = 65- 19.5
= 45.50
To find the total discount, take the original price and subtract the final cost.
Total discount = 85-45.50
= 39.50
To find the total percent discount, we use the formula
total percent discount = (original - final)/original * 100
= (85- 45.50)/85 * 100
= 39.5/85*100
= 46.47%
is there a proportional relationship between the area of an enlarged rectangle and the area of the original rectangle
F Gucci sells 47777,000 a month and if Chanel sells 4865,000 how much is together
Answer: 52,642,000
47777,000+4865,000
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Which inequalities are among the constraints for this situation?
Select each correct answer:
A. y≤25
B. x+y≥50
C. x+5y≤50
D. x≥5y
E. x≤5y
Answer: answers B and E and C are correct
Answer:
E. x ≥ 5y
A. y ≤ 25
B. x + y ≥50
Step-by-step explanation:
Let x represent the number of key chains.
Let y represent the number of thumb drives.
As we know that:
She wants to use at least 5 times as many key chains as thumb drives<=> x ≥ 5y
She has 25 thumb drives<=> y ≤ 25
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or key chain<=> x + y ≥50
So inequalities are among the constraints for this situation are:
x ≥ 5y
y ≤ 25
x + y ≥50
Escape what is on sale for 60% off the regular $80 price what is the sales price
Answer:
$32 is the sales price.
Step-by-step explanation:
First, change the percentage to a decimal.
60% = 60/100 = 0.6
Next, multiply 0.6 with the regular price ($80)
80 x 0.6 = 48
$48 is the discount. Subtract from the original price
80 - 48 = 32
$32 is the sales price.
~
Answer:
$32
Step-by-step explanation:
The sales price = original price - original price * discount rate
Factor out the original price
sales price = original price (1 -discount rate)
We know the original price is 80
We know the discount rate is 60% = .6
Substitute these values in
sales price = 80 (1-.6)
sales price = 80 * .4
sales price = 32
The cost of admission to the state fair changed from 8.50 last year to 10.00 this year.round to the nearest tenth show your work
A.what is the percent of change from last year to this year
B.is this a percent increase or decrease
C.if you have 25% off cpupon to ise on 10.00 ticket what is the cost
Answer:
A. What is the percent of change from last year to this year.
Answer: The percent of change from last year to this year is:
[tex]\frac{10.00 - 8.50}{8.50} \times 100[/tex]
[tex]\frac{1.50}{8.50} \times 100[/tex]
[tex]17.65 \%[/tex]
Therefore, the percent change from last year to this year is 17.65%
B. Is this a percent increase or decrease?
Answer: This is a percent increase.
C. If you have 25% off coupon to use on 10.00 ticket what is the cost?
Answer: The 25% of 10.00 is given below:
[tex]\frac{25}{100} \times 10.00[/tex]
[tex]0.25 \times 10.00[/tex]
[tex]2.5[/tex]
Therefore, the cost is:
[tex]10.00 -2.5 =7.5[/tex]
let f(x) = x^2 and g(x) = x − 3. evaluate (g ∘ f)(-2)
Answer:
(g ∘ f)(-2) = 1
Step-by-step explanation:
f(x)=x^2
g(x)=x-3
(g o f)(-2)=?
(g o f)(x)=g(f(x))
(g o f)(x)=g(x^2)
(g o f)(x)=(x^2)-3
(g o f)(x)=x^2-3
x=-2→(g o f)(-2)=(-2)^2-3
(g o f)(-2)=(-2)(-2)-3
(g o f)(-2)=4-3
(g o f)(-2)=1
If one class has 17 boys and 18 girls. If the ratio is the same in all classes in a total of 140 students how many girls are in the class?
Answer:
72 girls
Step-by-step explanation:
If a class has 17 boys and 18 girls, the total number of students in the class is
17+ 18 = 35
the ratio of girls to students is 18/35
Using the same ratio of girls to students
18 x
----- = ----------
35 140
We can solve this using cross products
18*140 = 35x
2520=35x
Divide each side by 35
2520/35 = 35x/35
72 =x
There are 72 girls
Find the distance between the points (5/2,3) and (3/2,8)
Answer:
d = [tex]\sqrt{26}[/tex] ≈ 5.1 ( to 1 dec. place )
Step-by-step explanation:
to calculate the distance d use the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = ([tex]\frac{5}{2}[/tex], 3) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 8)
d =√ ([tex]\frac{3}{2}[/tex] - [tex]\frac{5}{2}[/tex])² - (8 - 3)²
=[tex]\sqrt{1+25}[/tex] = [tex]\sqrt{26}[/tex] ≈ 5.1
A biased sample is one in which every member of the group has an equal chance of being chosen. True or false?
Answer:
false
Step-by-step explanation:
This statement is false, in a biased sample every member does not have an equal chance of getting selected.
What is a biased sample?If some individuals or groups from the population are not represented in the sample, the sample is biased.
Example of a biased sample:
The graph presented in the figure below, represents the drug usage by school students but this is a biased data because it does not include the students who have already passed out from the school or the students who were studying from home, as this data is not the complete data hence it is an example of a biased sample.
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if you flip a fair coin 6 times,what is the probability that you will get exactly 4 tails
The probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.
Explanation:To find the probability of getting exactly 4 tails when flipping a fair coin 6 times, we can use the binomial probability formula. The formula is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting k tails (in this case, k=4)n is the number of trials (in this case, n=6)p is the probability of getting a tail on a single trial (in this case, p=0.5)C(n, k) is the number of combinations of n things taken k at a time (in this case, C(6, 4) = 15)Plugging these values into the formula, we get:
P(X=4) = 15 * 0.5^4 * (1-0.5)^(6-4) = 15 * 0.0625 * 0.25 = 0.234375
So, the probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.
In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈ CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ , if P is the midpoint of CM
Answer:
CQ=4 cm, BQ=8 cm
Step-by-step explanation:
In given triangle ABC draw the line MD parallel to the AQ.
1. Consider triangle AMD. In this triangle PQ║MD (build) and CP=PM (P is midpoint of CM). Then by the triangle midline theorem, line PQ is midline of triangle AMD and CQ=QD.
2. Consider triangle BAQ. In this triangle AQ║MD and AM=MB. Then by the triangle midline theorem, line MD is midline of triangle BAQ and BD=QD.
Hence, CQ=QD=BD. Since BC=12 cm and
BC=BQ+QD+BD,
then
[tex]CQ=QD=BD=\dfrac{12}{3}=4\ cm.[/tex]
Note that
BQ=BD+QD=4+4=8 cm.
Final answer:
By examining the properties of median CM and midpoint P, we conclude that segment CQ is equal to QB, and both are 6 cm long in △ABC since CM bisects AB and BC is given as 12 cm.
Explanation:
The problem involves a triangle △ABC with CM being a median to side AB, and a line segment AP that intersects BC at point Q. According to the given information, P is the midpoint of CM, which implies that CP is equal to PM. Because BC is 12 cm in length, and CM is a median, we deduce that M is the midpoint of AB. This fact leads us to conclude that the triangles △CMB and △CMA are congruent by the Side-Side-Side (SSS) postulate, which means that CQ is equal to QB, and both are 6 cm long since Q lies on BC.
is the length of MN on graph
Answer:
mn=[tex]\sqrt{40}[/tex]
Step-by-step explanation:
m(2,5)n=(4,-1)
[tex]mn^{2}[/tex]=[tex](4-2)^{2}[/tex]+[tex](5+1)^{2}[/tex]
[tex]mn^{2}[/tex]=40
mn=[tex]\sqrt{40}[/tex]
what is the value of X
We know: The sum of measures of a tringle is equal 180°.
Therefore we have the equation:
m∠SQR + 58° + 35° = 180°
m∠SQR + 93° = 180° subtract 93° from both sides
m∠SQR = 87°
Angles SQR and PQR are supplementary. The sum of the measures of supplementary angles is 180°.
Therefore:
x + 87 = 180 subtract 87 from both sides
x = 93This is #5
Algebra-Find the value for x
I know it’s 11 but how do I get there.
Answer:
x = 11
Step-by-step explanation:
the line x + 5 is a mid segment of the triangle and thus is half the length of 3x - 1, that is
x + 5 = [tex]\frac{1}{2}[/tex](3x - 1)
multiply both sides by 2 to eliminate the fraction
2x + 10 = 3x - 1 ( subtract 3x from both sides )
- x + 10 = - 1 ( subtract 10 from both sides )
- x = - 11 ( multiply both sides by - 1 )
x = 11
Nala has 5,000 customers now she has 100 how many customers did she went away
Nala had lost 4,900 of her customers.
Hope this helps!
Answer:
Nala served 4,900 customers.
Step-by-step explanation:
5,000 to 100
5,000-100=4,900
YaY!!! u got it!!!! =)
What is the equation of the line-2,3 and 2,7
Answer:
The equation of the line that passes through the points (-2, 3) and (2, 7) is x - y + 5 = 0.
Step-by-step explanation:
Help please ?
What is the missing statement in the two column proof ?
You are correct. The answer is choice D
BD = BD by the reflexive property, which says that any segment is equal to itself
The hinge theorem says that the larger an angle is, the larger the opposite side will be. The converse goes in the opposite direction: if the side is larger, then the opposite angle is larger.
please help me in solving this
Answer:
a = 8, b= - 48, c = - 16
Step-by-step explanation:
multiply through by 8x² to eliminate fractions
[tex]x^{5}[/tex] - 16 = 48x² - 8x³ ( subtract 48x² - 8x³ from both sides )
[tex]x^{5}[/tex] + 8x³ - 48x² - 16 = 0
compare the coefficients of like terms to
[tex]x^{5}[/tex] + ax³ + bx² + c = 0
⇒ a = 8, b = - 48, c = - 16
Divide fractions with thinking blocks
Answer:
draw out your diagram... if it was 1/2 draw one long shape (say it's a rectangle) and cut it once
Step-by-step explanation:
===/===
it should look something like this (represents 1/2)