Answer:
9/20
Step-by-step explanation:
Total number of candies =60
Number of Green candies, n(G)=36
Number of candies with caramel, n(C)=45
Since the events are independent, the probability of selecting two candies where the first is green and the second has caramel is given by:
P(GC)=P(G) X P(C)
\begin{gathered}=\dfrac{n(G)}{n(S)} X \dfrac{n(C)}{n(S)} \\=\dfrac{36}{60} X \dfrac{45}{60}\\ =\dfrac{9}{20}\end{gathered}=n(S)n(G)Xn(S)n(C)=6036X6045=209
The probability in its lowest form is 9/20.
find the least number that must be subtracted from 21 2o show the result is a perfect square
Answer:
5
Step-by-step explanation:
2 × 2 = 4
3× 3 = 9
4 × 4 =16
5 × 5 =25
16 is the only number and closest number to 21 to subtract from
HELP QUICK! You must find all intervals
where f(x) is negative.
f(x)=2(x+3)(x-7)
Answer:
any # where -2<=x<7
Step-by-step explanation:
(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.
which variable expression describes the area of the shaded region in the diagram shown below ?
Answer: B
Step-by-step explanation:
The area of entire rectangle is (9)(4)=36.
The area of the square inside is [tex]x(x)=x^2[/tex]
Subtracting the areas, we get [tex]36-x^2[/tex]
James needs to mix a 10% acid solution with a 50% acid solution to create 100 milliliters of a 26% solution. How many milliliters of each solution must James use?
James must mix _____ milliliters of 10% solution and____milliliters of 50% solution.
James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.
Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.
Now,
10% x + 50% ( 100 - x ) = 26% ×100
⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]
⇒10x + 50( 100 - x ) = 2600
⇒10 x + 5000 - 50x = 2600
⇒10 x - 50 x = 2600-5000
⇒-40 x = -2400
⇒x=60
Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.
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2 In the diagram below of AABC, TV || BC, AT = 5,
TB = 7, and AV = 10.
B
A
What is the length of VC?
1) 3-1/2
2) 7-½-1
3) 14
4) 24
C
4
Answer:
14
Step-by-step explanation:
AT/TB = AV/VC
5/7 = 10/VC
VC = 14
For the given figure length of VC = 14.
In the given figure,
We can see that,
ΔATV and ΔABC are similar triangle,
Since we know that,
Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The '' sign here denotes the resemblance of triangles.
Therefore,
AT/TB = AV/VC
It is given that,
AT = 5
TB = 7
AV = 10
Now put these values we get,
⇒ 5/7 = 10/VC
⇒ VC = 14
Hence,
Length of VC is 14 units.
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Jenny likes to paint. she estimates the number of paintings she completes using the function p of w equals one half times w plus one, where w is the number of weeks she spends painting. the function j(y) represents how many weeks per year she spends painting. which composite function would represent how many paintings jenny completes in a year?
The composite function of the paintings Jenny completes in a year is
[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
What is a composite function?A composite function is a function made of other functions, where the output of one function is the input to the other function.
An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]
We have [tex]P(w)=\frac{1}{2}w+1[/tex]
Here, P(w) represents the number of paintings Jenny completes in some w weeks. and
J(y) represents the number of weeks per year.
As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting
w as J(y) in the equation we have
Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]
Hence this is the composite function that would represent the number of paintings Jenny completes in a year.
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Question
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third
side of each triangle.
с
y = c =
6.5
Provide your answer below:
A
12
C
B
Z
y
4.8
3
Y
Answer:
AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle
Estimate the cost of painting a concrete patio if it is a 12 foot by 12 foot rectangle, and a quart of paint that covers 47 square feet costs $11.99.
Answer: $36.68 or $35.97. Read below.
Step-by-step explanation: You need to multiply the 12 foot by 12 foot and you would get 144 sq feet. Then divide 47 into 144. You will be left with 3.06, and if you need to round, you can round that to 3. Then you need to multiply 3 by $11.99 and you will be left with the cost for the paint, which is $35.97 if you do round to a three, and $36.68 if you do not round the three. So your answer is either $36.68 or $35.97 depending on whether you round or not.
Find f(−1) given f(x)=−3x3+2x2+24
A. -23
B. 28
C. 29
D. 23
Answer:
C. 29
Step-by-step explanation:
[tex]f(x) = -3x^3 + 2x^2 +24[/tex]
• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:
[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]
⇒ [tex]-3(-1) +2(1) + 24[/tex]
⇒ [tex]3 + 2 + 24[/tex]
⇒ [tex]29[/tex]
[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]
We have this equation:
[tex]f(x)=-3x^3+2x^2+24[/tex]
Substitute [tex]x=-1[/tex]:
[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]
Simplify to find the final answer:
[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]
Instructions: Determine if AB is tangent to the circle.
AB
20
B
12
수 to the circle.
16
Step-by-step explanation:
to be a tangent, it would have to have a 90° angle with the radius (12).
and that would make the triangle ABCenter of the circle a right-angled triangle.
and then Pythagoras must apply :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle). in our case the 20-line.
so,
20² = 12² + 16²
400 = 144 + 256 = 400
yes, it is confirmed, because the Pythagoras principle applies, it is a right-angled triangle, and therefore AB is indeed a tangent.
Answer:
the line AB is tangent to the circle
Step-by-step explanation:
we have :
16² + 12² = 256 +144 = 400
On the other hand:
20² = 400
Then
16² + 12² = 20²
Then
According to the Pythagorean theorem:
The line AB is perpendicular to the radius of the circle
Which means the line AB is tangent to the circle.
Which graph represents this inequality Y is greater than or less to 4X -3
The graph of the inequality can be seen in the image at the end.
Which graph represents the inequality?
Here we have the inequality:
y ≥ 4x - 3
To graph this we need to graph the line:
y = 4x - 3
With a solid line (because the points on the line are solutions) and then shade the region above that line.
The graph of the inequality can be seen below.
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7. How many triangles exist when the angle measures are 90°, 90°, and 0°? 2 POINTS
Answer: None
Step-by-step explanation:
There is no triangle with an angle measure of 0 degrees.
Write an expression that is equivalent
1/2a-4
Step-by-step explanation:
Answer
a - 8
------------+
2
If [tex]\frac{w}{y} = \frac{y}{z} then what is the value of x?[/tex]
The value of x in the given expression is; x = wz/y
How to change subject of formula?We are given the expression;
w/x = y/z
Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;
Multiply both sides of the given expression by x to get;
(w/x)*x = (y/z)*x
⇒ w = xy/z
Now, multiply both sides by z/y to get;
w(z/y) = (xy/z) * (z/y)
wz/y = x
Thus, the value of x in the given expression is;
x = wz/y
The correct question is;
If w/x = y/z, then what is the value of x
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A school year begins with 24 students
trying out for the basketball team and 20
students trying out for the debate team.
Within a week, 6 students have dropped
out of the basketball tryouts and 2
students have dropped out of the debate
tryouts. What percentage of the remaining
students are trying out for the basketball
team?
Answer:
50%
Step-by-step explanation:
In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%
The amount of money spent buying packets of instant noodles varies directly
with the number of packets purchased. If 30 packets of noodles cost $34.88,
how much would 45 packets cost? Round all answers to the nearest hundredth
in your calculations.
A. $38.70
B. $52.20
C. $25.83
D. $43.00
The cost of 45 packets of instant noodles given the direct variation is $52.335
Direct variationlet
Amount spent on noodles = nNumber of Packets purchased = pn = k × p
Where,k = constant of proportionality
34.88 = k × 30
34.88 = 30k
k = 34.88/30
k = 1.16266666666666
Approximately,
k = 1.163
Find n when p = 45
n = k × p
= 1.163 × 45
n = $52.335
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F THREE DIAGONALS ARE DRAWN INSIDE A HEXAGON WITH EACH ONE PASSING THROUGH THE CENTER POINT OF THE HEXAGON, HOW MANY TRIANGLES ARE FORMED?
If three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.
Diagonals in a hexagonThere are nine diagonals in a regular hexagon
But for one with three diagonals drawn through the center, six equilateral triangles are formed.
Thus, if three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.
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Write an equation of a circle with the given center and radius. Check your
answers,
(-4,-6), 7
Answer: [tex]\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]
Work Shown:
[tex](h,k) = (-4,-6) = \text{center}\\\\r = 7 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - (-4))^2 + (y - (-6))^2 = 7^2\\\\\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]
To check the answer, you can use a graphing calculator like GeoGebra or Desmos or similar.
The function g(x) = 10x2 100x + 213 written in vertex form is g(x) 10(* - 5)2 - 37. Which statements are true
about g(x)? Select three options.
The axis of symmetry is the line x = -5.
The vertex of the
graph is (5, -37).
The parabola has a minimum.
The parabola opens up.
.
The value of a, when the equation is written in vertex form, is negative.
Answer:
Step-by-step explanation:
The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos
It looks to me that the equation is g(x) = 10(x - 5)^2 - 37
I checked to see that this is correct, and thank goodness it is.
The vertex of the graph is (5, -37).The vertex has a minimumThe parabola opens upwardThe graph is shown below.
The sum of two numbers is 21. Three times the larger is equal to four times the smaller.
Find them.
Find the equation of a straight line which passes through the point (3, 2) and is perpendicular to the line 3x + 5y =10. Hence, determine the gradient and y-intercept of the equation.
Answer:
Step-by-step explanation:
eq of line perpendicular to 3x+5y=10 is
5x-3y=a
where a is constant.
it passes through (3,2)
5(3)-3(2)=a
a=15-6=9
reqd. eq. is 5x-3y=9
or
3y=5x-9
y=5/3 x-3
gradient=5/3
y-intercept=-3
or
5y=-3x-10
y=-3/5 x-2
slope=-3/5
slope of reqd. line=-1/(-3/5)=5/3
eq. of line through (3,2) is
y-2=5/3(x-3)
3y-6=5x-15
3y=5x-15+6
3y=5x-9
y=5/3 x-3
A company pays $10 per hour for up to eight hours of work. What is the equation for total pay why for hours for ex for 0 to 8 hours of work X
The equation for total pay is y = 10/8x.
What is the equation?Division is the mathematical operation that is used to determine the quotient of a number. In order to determine the total pay for hours from 0 to 8, the pay per hour has to be determined. To determine this value, divide $10 by 8.
Pay per hour = $10 / 8
y = 10/8x.
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Question 16 of 50
Jayden received a bonus check from his work for $6,000. He is going to deposit the money into a bank account that receives 5% compounded annually.
The amount of interest earned after year 5 is:
O $7,657
O $8,421
O $7,300
if one adult is randomly chosen from the group, what is the probability that the adult does not use a cell phone app for shopping and is at least 40 years old?
Answer:
1/100
Step-by-step explanation:
The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.
Ps: Sorry if this is wrong, this is just a guess.
HELP ME!!!!Question 13 of 25
What is the approximate value of tan B?
h
17.46
16
A. 2.29
B. 0.40
C. 0.44
D. 0.92
Answer: A
tan= Opposite ÷ Alternate
tan B= 16 (which is the opposite side of B) ÷ 7 (it's the side beside B, excluding 17.46 as it's the hypotenuse)
Therefore 16÷7 = 2.285714286
= 2.29 (3sf)
Answer:
just choose one
SOMEONE PLS ANSWER STEP BY STEP TY
9k-2≥88 or -34 -4> -25
Hello,
9k - 2 88
⇔ 9k - 2 + 2 ≥ 88 + 2
⇔ 9k ≥ 90
⇔ 9k/9 ≥ 90/9
⇔ k ≥ 10
S = [10 ; + ∞ [
Answer:
k ≥ 10
Step-by-step explanation:
9k - 2 ≥ 88
Step 1 : Add 2 on both sides.
9k - 2 + 2 ≥ 88 + 2
9k + 0 ≥ 90
9k ≥ 90
Step 2 : Divide 9 on both sides.
9k/9 ≥ 90/9
k ≥ 10
please can you help me?
Answer:
A) 65
B) 60
Step-by-step explanation:
64.9963 rounds to 65
To the nearest 10 it would round down as the second intiger the 4 is below 5 meaning as a result it rounds down
After rounding the given number 64.9963:
(a) Near 2 decimal places is: 64.70
(b) And the nearest 10 is: 60
When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
The given number is:
64.9963
To round off the nearest 2 decimal places:
Since the third digit after the decimal is 6 which is greater than 5.
Add 1 to their previous digit.
Therefore,
After rounding near to 2 decimal places the number becomes:
64.70
To round off the nearest 10:
Since the tense digit is 4 and it is less than 5
Therefore,
The number after rounding off the nearest 10 is:
60.
Hence, after rounding the number:
Near 2 decimal places is: 64.70
And the nearest 10 is: 60
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An angle measures 87.6° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
1.2° and 88.8°Step-by-step explanation:
Complementary angles are angles that add up to 90°.
Let's say angle 1 is x, and angle 2 is 87.6 less than x.
We already know that angle 1 + angle 2 = 90, so we can just substitute x now.
We know that complementary angles add up to 90, so one of the angles is 90-x, and the other one is 90-x-87.6.
x = (90 - x) - 87.6
Simplifies to:
x = 2.4-x
Add x to both sides
2x = 2.4
Divide by 2
x = 1.2
To get the other angle, add 87.6 to 1.2
1.2+87.6 = 88.8
So, angle1 = 1.2, and angle2 = 88.8
Let's check our work.
88.8 + 1.2 = 90, so the angles are complementary and have a difference of 87.6
Hope this helps (:
Answer:
1.2°, 88.8°
Step-by-step explanation:
let one angle=x
other angle=y
y=x-87.6
also
x+y=90
x+x-87.6=90
2x=90+87.6=177.6
x=88.8
other angle=88.8-87.6=1.2
Which expression is equivalent to
The expression is equivalent to 2 , option C is the right answer.
What is an Expression ?An expression in maths is a statement that contains , constants , variables and mathematical operators.
The expression given in the question is
[tex]\rm \dfrac { 4^{\frac{5}{4}} * 4^{\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]
Applying exponent rule
[tex]\rm a^m * a^n = a^{m+n}[/tex]
[tex]\rm \dfrac { 4^{\frac{5}{4} +\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]
Applying exponent rule
[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]
[tex]\rm { 4^{\frac{5}{4} +\frac{1}{4} -{\frac{1}{2}}}[/tex]
On solving the exponents
=(6/4) -(1/2)
=4/4
=1
=[tex]\rm 4^{\frac{1}{2}}[/tex]
= 2
Therefore the expression is equivalent to 2 , option C is the right answer.
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melissa worked 7 hours and 40 minutes last monday. she makes 16 dollars and hour.how much did she make for those hours she worked on that day?