Answer:
Step-by-step explanation:
Here, I will instead go through the process for finding the probability of choosing two girls. Then once you understand how it was done, hopefully you will be able to answer the actual question for yourself.
Finding the probability of choosing two girls. Let's make it simpler by starting with the probability of choosing the first girl only.Probability of choosing the first girl. (Note: the letter chosen to represent the event is not important. Pick something that makes sense to you and be consistent)
P(G1) = # of girls / # of total outcomesSo the number of girls we know to be 11. What is the number of total outcomes? Well a boy or a girl can be chosen, and there are 14 boys and 11 girls, for a total of 25 students.
P(G1) = 11/ 25Let's find the probability of choosing the second girl from here.
P(G2) = # of girls / # of total outcomesHowever, this time things have changed. We've already chosen one girl, so the number of girls remaining to choose from is reduced 11 to 10. And the total number of students to choose from is reduced from 25 to 24.
P(G2) = 10 / 24Now we have the probability of choosing the first girl and the probability of choosing the second girl. From here, we just need to combine them to find the probability of both things happening together. To calculate the probability of two different events occurring, you multiply the two probabilities together.
Probability of choosing two girls. Let's use T for Two girls.
P(T) = P(G1) × P(G2) = (11 /25) × (10/24)
From here you can use a calculator to find the answer. This answer can either be written as a fraction, a decimal, or a percentage.
= 0.19 = 19 / 100 = 19%
Parallelogram RSTU is shown. The perimeter of parallelogram RSTU is 50
centimeters. What is the value of x? *
R.
(2x + 15) cm
S
(3x + 20) cm
U
T
-5
-2.
3
O 12
Answer: x = -2
Step-by-step explanation:
Given:
Perimeter = 50 cm
=> 2 (2x+15)+ 2(3x+20) =50
=> 4x+30+6x+40=50
=> 10x= -20
=> x= -20/10
=> x = -2
Write the equation in slope-intercept form. y=−5(x+6)+2x
Answer:
y = −3x −30
Step-by-step explanation:
Slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)y = −5(x + 6) + 2x <== distribute -5
y = −5(x) + −5(6) + 2x
y = −5x −30 + 2x <== combine like terms
y = −3x −30
y = −3x −30
-3 = slope-30 = y-intercept (0, -30)Hope this helps!
eter and Area
5
Annita is sewing a lace edge around a rectangular quilt. She will need 160 inches of lace to do the entire quilt. If the quilt is 46
inches wide, how long is the quilt?
A. 32 inches
B. 34 inches
C. 80 inches
D.
68 inches
Reset
Submit
Answer:
B. 34 inches
Step-by-step explanation:
its 34 inches because you do 46x2 because of the two sides and you will get 92. Then subtract 92 from 160 to find out the other side and you will get 68. Then do 68÷2 because you have to find the other side and you will get 34
One number is 4 more than another number. If the greater number is x, what is the other number?
first number: x
second number: x -4
Write an equation of the line that passes through (-1,3) and is parallel to the line y=2x+2 .
Answer:
y = 2x + 5
Step-by-step explanation:
REMEMBER:
The new line will be parallel to the line represented by y =2x +2⇒ The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope. So the slope of this line is 2. A line parallel to y = 2x + 2 will have the same slope. This means the slope of the new line will also be 2.
To determine the equation of the new line, we can use the given point to find the y intercept of the new line:
⇒ y = 2x + b
Use x = -1 and y =3 to find b (or the y intercept ) of the new line:
⇒ 3 = 2 * (-1) + b
⇒ 3= -2 + b
⇒ b=5
Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:
⇒ y = 2x + 5
Answer:
y = 2x + 5
Step-by-step explanation:
Given line equation 2x - y + 2 = 0
Equation of line parallel to this line will be of form
=> 2x - y + k = 0 ( where 'k' is a constant )
Now this line passes through (-1,3)
=> 2(-1) - (3) + k = 0
=> -2 - 3 + k = 0
=> k - 5 = 0
=> k = 5
Therefore the required line equation is 2x - y + 5 = 0 or y = 2x + 5
Hope you've understood the solution.
Solve for x
2x3=x2+6x
please help me. Thanks
Answer:
heya! ^^
[tex]2x {}^{3} = x {}^{2} + 6x \\ \\ 2x {}^{3} = x(x + 6) \\ \\ dividing \: both \: sides \: by \: x \\ \\ \frac{2\cancel{x} {}^{3} }{\cancel{x}} = \frac{\cancel{x}(x + 6)}{\cancel{x}} \\ \\ 2x {}^{2} = x + 6 \\ \\ 2x {}^{2} - x - 6 = 0 \\ \\ by \: splitting \: the \: middle \: term \: ( - x) \\ \\ 2x {}^{2} - 4x + 3x - 6 = 0 \\ \\ 2x(x - 2) + 3(x - 2) = 0 \\ \\ 2x + 3 = 0 \: \: \: or \: \: \: (x - 2) = 0 \\ \\ x = \frac{ - 3}{2} \: \: \: \: or \: \: \: \: x = 2[/tex]
hope helpful :D
Assuming that Dave’s marginal tax bracket is 25%, but how much did his federal taxes declined this year if he contribute 7000 to his retirement account?
The marginal tax bracket of Dave shows that the amount of the federal tax is $28000.
How to compute the tax?Let the federal tax be represented by x.
From the information, Dave’s marginal tax bracket is 25%, and he contributed 7000.
Based on the information, the amount will be:
25% of x = 7000
0.25 × x = 7000
0.25x = 7000
x = 7000/0.25
x = $28000
In conclusion, the amount is $28000.
Learn more about tax on:
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The measures of two angles of a triangle are 29° and 61°. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation.
I know that the answer is 27 and that 3 + x = 7 but where do you get 4?
Answer:
27
step by step explanation
if you are calculating for the area of the figure, divide the shape into two figures and you will get two rectangles
for shape 1
length=3 width=5
for shape2
length 7-3=4
width=3
area of shape1. =3×5=15
area of shape2. =4×3=12
area of the shape= 12+15 = 27
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).
Answer:
The only true statement is :
The graph of the function is a parabola
Step-by-step explanation:
f(x) = x² – 5x + 12
Option 1: The value of f(–10) = 82
Reason : f(-10) = (-10)² – 5(-10) + 12 = 100 + 50 + 12 = 162 ≠ 82
Option 2: The graph of the function is a parabola [tex]\huge\checkmark[/tex]
Option 3: The graph of the function opens down
Reason : the coefficient of x² is 1 ,which is a positive number then the graph opens up.
Option 4: The graph contains the point (20, –8)
Reason : f(20) = 312 ≠ -8
Option 5: The graph contains the point (0, 0)
Reason : f(0) = 12 ≠ -8
Answer:
ABC
Step-by-step explanation:
A rabbit runs 35 feet in 7 seconds, a cat runs 18 feet in 2 seconds. Who is faster?
Answer:
The cat is faster.
Step-by-step explanation:
Compare the animals' speeds in feet per second.
Rabbit:
feet/sec = 35/7
= 5ft/sec
Cat:
feet/sec = 18/2
= 9 ft/sec
9 ft/sec is faster than 5ft/sec.
The cat is faster.
URGENT I HAVE ALMOST 0 TIME LEFT I NEED LAST MINUTE HELP
A parabola has zeros of 7 and 1 and passes through the point (3,4). Determine the equation of the parabola.
Answer:
The zeros are the points where the parabola intercepts the x-axis.
[tex]\sf x = 7 \implies x - 7 = 0[/tex]
[tex]\sf x = 1 \implies x - 1 = 0[/tex]
[tex]\sf \implies y = a(x - 7)(x - 1)[/tex] where a is some constant
If the parabola passes through point (3, 4) then:
[tex]\sf \implies a(3 - 7)(3 - 1) = 4[/tex]
[tex]\sf \implies a(-4)(2) = 4[/tex]
[tex]\sf \implies -8a = 4[/tex]
[tex]\sf \implies a = -\dfrac12[/tex]
So the equation of the parabola is:
[tex]\sf y = -\dfrac12(x - 7)(x - 1)[/tex]
Or in standard form:
[tex]\sf y = -\dfrac12x^2+4x-\dfrac72[/tex]
Spot the quadratic equation:-
(x-1)(x-7)x(x-7)-1(x-7)x²-7x-x+7x²-8x+7Find a through (3,4)
a(x²-8x+7)=4a(9-24+7)=4a(-8)=4a=-1/2Equation:-
y=-1/2(x-7)(x-1)On Friday, Hayley has purchased more flour and eggs, but only has 22 cups of sugar and 4 sticks of butter. Which combination of loaves of zucchini bread and banana bread can Hayley make?
Answer:
It is C
Step-by-step explanation:
The points (-1, r) and (4, 6) lie on a line with slope 3. Find the missing coordinate r.
Answer:
R = -9
Step-by-step explanation:
To solve the slope with two points, you would use the formula y2 - y1/x2 - x1. First, you would take the formula and sub in the values that you currently know.
6 - r/4 - (-1) = 3, 6 - r/5 = 3, 6 - r = 15, -r = 9, r = -9
Therefore, r = -9.
Nancy put new insulation in her attic and discovered that her heating bill for December decreased from $160 to $100. What is the percent decrease?
The amount of decrease is ______?
Answer:
37.5% decrease
Step-by-step explanation:
To find a relative percentage you generally follow the rule of part divided by whole.
$100 / $160 = .625 (62.5%)
So $100 is 62.5% of $160
To find the decrease we need to subtract 62.5% from 100%
100 - 62.5 = 37.5
A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 5900 dollars?
nt
A = P(1+)
The time required to get a total amount of $5,900.00 with compounded interest on a principal of $5,000.00 at an interest rate of 5.75% per year 2.899 years
Compound InterestGiven Data
Principal P = $4000Rate r= 5.75%Final Amount A = %5900Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(5,900.00/5,000.00) / ( 4 × [ln(1 + 0.0575/4)] )
t = ln(5,900.00/5,000.00) / ( 4 × [ln(1 + 0.014375)] )
t = 2.899 years
Learn more about compound interest here:
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The circumference of circles
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's find the circumference of given circle ~
Circumference :
[tex]\qquad \tt \dashrightarrow \: \pi{d}^{}[/tex]
where, d = diameter
Now, let's calculate it ~
[tex]\qquad \tt \dashrightarrow \: c = 4×\pi{}^{}[/tex]
[tex]\qquad \tt \dashrightarrow \: c = 4\pi\: \: in[/tex]
That's the answer I terms of π, but we can also plug in the approximate value of pi as 3.14
[tex]\qquad \tt \dashrightarrow \: c = 4 \times 3.14{}^{} \\\qquad \tt \dashrightarrow \: c = 12.56\: \: in\\\qquad\tt \dashrightarrow \: c \approx 12.6\: \: in[/tex]
. A recipe that serves 6 people calls for 4 cups of milk. How many cups of milk are needed to serve 15 people?
Answer:
10 cups
Step-by-step explanation:
6 people : 4 cups
15 people : x cups
15/6 = 2.5
4 x 2.5 = 10 cups
Hope this helps :)
(And sorry before, I was a little mixed up)
Answer:
10
Step-by-step explanation
What is the slope of a line perpendicular to the line whose equation is
5x – 2y = -10. Fully simplify your answer.
Answer:
-2/5
Step-by-step explanation:
5x - 2y = -10
-2y = -5x - 10
y = 5/2x + 5
m = 5/2
Perpendicular lines have slopes that are negative reciprocals of one another. For example, 5 would become -1/5 and 1/3 would become -3.
If m = 5/2
Perpendicular line m = -2/5
Hope this helps!
Answer:
The slope of the line perpendicular to this line is -2/5.
Step-by-step explanation:
5x - 2y = -10
Let's simplify this equation to be in slope-intercept form: y = mx + b.
Start by adding 2y to both sides of the equation.
5x = -10 + 2yNext, add 10 to both sides of the equation.
5x + 10 = 2yDivide both sides of the equation by 2.
(5x + 10)/2 = y (5/2)x + 5 = yThe slope of this line is the coefficient of x; in this case, it is 5/2.
If we want to find the slope of the line perpendicular to this line, we take the opposite (change the sign) reciprocal (flip the fraction).
The slope 5/2 becomes -2/5.
Therefore, the slope of a line perpendicular to the line whose equation is 5x - 2y = -10 is -2/5.
what is 22 percent of 198
Answer:
43.56
Step-by-step explanation:
22 percent of 198 can be found by converting 22 percent into decimal form which is
22% = 0.22
because a 100% = 1
Then we can multiply 0.22 by 198
0.22*198 = 43.56
So the answer is 43.56
Hope this helps! :)
Another math question for you guys
Answer: 65 Degrees
Hope this helps :)
If so brainliest would mean alot thanks!
Step-by-step explanation:
35/ 65 degrees
Pretty sure it's 65
Answer: 25 degrees
Step-by-step explanation: Angle ATC equals 90 degrees 90 - 65 = 25
Find the surface area
Answer:
The answer is : 8160 m
Step-by-step explanation:
100% correct
Two cards are chosen at random without replacement from a pack of 52 playing cards. If the first card chosen is an Ace, what is the probability the second card chosen is a King?
Answer:
4/52 or 1/13
Step-by-step explanation:
Answer:
the probabilyy of that will probably be the probability of that question porbably speaking about probability
make y the subject...
Answer:
y = qx/p -qr
Step-by-step explanation:
To solve for a variable, you must undo the operations done to the variable. Here, the variable is divided by a negative number (-q), and the result is added to another term (x/p).
We undo the addition by adding the opposite of the term that is added:
[tex]\dfrac{x}{p}-\dfrac{x}{p}-\dfrac{y}{q}=r-\dfrac{x}{p}\qquad\text{add $-\dfrac{x}{p}$}\\\\-\dfrac{y}{q}=r-\dfrac{x}{p}\qquad\text{simplify}[/tex]
We undo the division by multiplying by the reciprocal of the coefficeint, -q.
[tex]\left(-\dfrac{y}{q}\right)(-q)=\left(r-\dfrac{x}{p}\right)(-q)\qquad\text{multiply by $-q$}\\\\\boxed{y=-qr+\dfrac{qx}{p}}\qquad\text{simplify}[/tex]
Un terreno rectangular cuyo ancho mide 20 mts menos que su largo. Su área del terreno es de 150 metros cuadrados. ¿Determina las medidas del largo y del ancho?
Answer:
you are a good friend Sayed im not sure if I can get it done before I get my license back and the whole time we go back and be out in a bit I guess that was the best thing I ever heard of the beast's I have
The triangle shown below has an area of 16 units^2 squared.
Find the missing length.
x = ______ units
Answer:
8 units
Step-by-step explanation:
Given:
Base = 4 unitsHeight = x unitsArea of triangle = 16 units²Formula:
[tex]\text{Area of triangle:} \ \dfrac{1}{2} \times \text{Base} \times \text{Height}[/tex]
Substitute the base, height and the area of the triangle to determine the measure of the height (x).
[tex]\implies 16 \ \text{units}^{2} = \ \dfrac{1}{2} \times 4\times x[/tex]
Simplify the right hand side of the equation.
[tex]\implies 16 \ \text{units}^{2} = \ 2\times x[/tex]
Divide both sides by 2 to isolate "x".
[tex]\implies \dfrac{16 \ \text{units} }{2} = \dfrac{2\times x}{2}[/tex]
[tex]\implies 8 \ \text{units} = x[/tex]
The measure of the height (x) is 8 units.
Answer: 8
Step-by-step explanation:
The circumference of the circle is 24 cm and the radius is √x+2. Find x and its radius. Use = 3.14 . Round your answer to two decimals.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Circumference of a circle :
[tex]\qquad \tt \dashrightarrow \:2 \pi r[/tex]
And we have been given that Circumference = 24 cm
So, let's equate them and find radius (r) :
[tex]\qquad \tt \dashrightarrow \:2 \pi r = 24[/tex]
[tex]\qquad \tt \dashrightarrow \:r = \dfrac{ 24}{2 \pi}[/tex]
[tex]\qquad \tt \dashrightarrow \:r = \dfrac{ 12}{3.14}[/tex]
[tex]\qquad \tt \dashrightarrow \:r = 3.82 \: \: cm[/tex]
So, we got the radius here. now let's equate it with expression in terms of x to find value of x
[tex]\qquad \tt \dashrightarrow \: \sqrt{x + 2} = 3.82[/tex]
[tex]\qquad \tt \dashrightarrow \:{x + 2} = (3.82) {}^{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:{x } \approx 14.59 - 2[/tex]
[tex]\qquad \tt \dashrightarrow \:{x } \approx 12.59 \: \: cm[/tex]
x = 12.61
===========
[tex]\bold{C = 2\pi r}[/tex] [ C = 24, π = 3.14, r = √x+2 ]
2(3.14)(√x+2) = 24(6.28)(√x+2) = 24√x+2 = 24/6.28x+2 = (24/6.28)²x = (24/6.28)² - 2x = 12.60505497x ≈ 12.61 ( rounded to nearest two decimal places )
A rectangular box has a volume of 15 cubic feet. The length, width, and height of the box are each doubled.
What is the new volume of the rectangular box?
O A. 30 cubic feet
OB. 60 cubic feet
O c. 90 cubic feet
OD. 120 cubic feet
Answer:
I BELIEVE the answer would be 30
A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
Please explain how to solve this problem, not just the answer.
The area of the square pyramid building is the amount of space on it
The maximum base length of the building is 67.42 cm
How to determine the maximum side length?The given parameters are:
Base = b
Slant height (l) = 5b
The lateral surface area is calculated using:
L = 2bl
So, we have:
L = 2 * b * 5b
Evaluate the product
L = 10b^2
The total surface area is calculated using:
T = L + b^2
So, we have:
T = 10b^2 + b^2
Evaluate the sum
T = 11b^2
The maximum surface area is 50,000 square feet
So, we have:
11b^2 = 50000
Divide both sides by 11
b^2 = 50000/11
Take the square root of both sides
b = 67.42
Hence, the maximum base length of the building is 67.42 cm
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Answer: 71 feet
Step-by-step explanation:
Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.
The lateral surface area of a square pyramid can be calculated using the formula:
Lateral surface area = (perimeter of base) × (slant height) / 2
The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:
Lateral surface area = 4x × (5x) / 2 = 10x^2
We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:
20,000 ≤ 10x^2 ≤ 50,000
Dividing both sides by 10, we get:
2000 ≤ x^2 ≤ 5000
Taking the square root of both sides, we get:
44.7 ≤ x ≤ 70.7
Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.
Therefore, the maximum possible side length of the base of the building is 71 feet.
I think of a number, add 5,then square the answer. The result is 100. What could the number be?
x=
x=
Answer:
x = 5
x = -15
Explanation:
Let the number be "x"
===================
(x + 5)² = 100x + 5 = ±√100x + 5 = ±10x + 5 = 10, x + 5 = -10x = 10 - 5, x = -10 -5x = 5, -15Answer:
x= 5 or -15
Step-by-step explanation:
let the number be x
(x+5)^2=100
x^2+10x+25=100
x^2+10x-75=9
look for factors of 75 that when you gives you 10 and when you multiply gives you -75
those factors are 15 and -5
replace 10x with 15x and -5x
x^2+15x-5x-75=0
then group them, and factorize
x(x+15)-5(x+15)=0
x-5=0 or x+15=0
x= 5 or x= -15