Problem 1
S = sample space = set of all possible outcomes
S = set of positive factors of 72
S = {1,2,3,4,6,8,9,12,18,24,36,72}
n(S) = number of items in sample space
n(S) = 12
E = event space = set of outcomes we want to happen
E = set of factors of 72 such that they are less than 10
E = {1,2,3,4,6,8,9}
n(S) = number of items in event space
n(S) = 7
P(E) = probability get a value in set E (that is also in set S as well)
P(E) = probability we get a positive factor of 72 that is less than 10
P(E) = n(E)/n(S)
P(E) = 7/12
Answer: 7/12============================================
Problem 2
[tex]\begin{array}{ccl}S & = & \text{Sample Space}\\\\S & = & \{\\ & & ~~DAB, DAC, DAE, DAF, DAG, DAH\\ & & ~~DBA, DCA, DEA, DFA, DGA, DHA\\ & & \}\end{array}[/tex]
n(S) = 12
E = event space
E = {DCA}
n(E) = 1
P(E) = probability we get an item in set S that is in set E also
P(E) = probability we get DCA from set S listed above
P(E) = n(E)/n(S)
P(E) = 1/12
Answer: 1/12McKenzie sells textbooks. She receives 7% on her first $1,000 in sales and 15% on the balance of her sales. How much would she earn in commission if her sales in one month were $14,500? Enter your answer as a dollar amount rounded to the nearest cent. Do not type a dollar sign symbol in the box.
The commission would be $2095.
Step-by-step explanation:
Given,
Commission on first $1000 = 7%
Amount of commission = 0.07*1000 = $70
Worth of sold items = $14,500
We will subtract $1000 from it.
Balance = 14500-1000 = $13500
Commission on balance = 15% = 0.15
Amount of commission = 0.15*13500
Amount of commission = $2025
Total commission = 70+2025 = $2095
The commission would be $2095.
Keywords: percentage, subtraction
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McKenzie would earn $2,095 in commission if her sales for the month were $14,500.
Explanation:To calculate McKenzie's commission, we need to determine the amount of sales that fall under the 7% rate and the amount that falls under the 15% rate. First, we calculate the commission on the first $1,000 in sales: 7% of $1,000 = $70. Next, we calculate the commission on the remaining sales: $14,500 - $1,000 = $13,500. 15% of $13,500 = $2,025.
Finally, we add the two commissions together to get the total commission: $70 + $2,025 = $2,095. So McKenzie would earn $2,095 in commission if her sales for the month were $14,500.
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256 to the nearest 100
Answer:
300.
Step-by-step explanation:
256 is closer to 300 than it is to 200 so it rounds to 300.
Answer:300
Step-by-step explanation:
I need help please and thank you
Answer:
∠A = 45°
Step-by-step explanation:
The sum of angles in a triangle = 180°.
That means in the triangle ABC, ∠A + ∠B + ∠C = 180°.
Given ∠B = 90° and ∠C = 45°.
⇒ ∠A + 90° + 45° = 180°
⇒ ∠A = 180 - 90 - 45
⇒ ∠A = 45° is the required answer.
I do not deed the answers for 11, or 12 just 13
13.
A
B
C
D
E
F
G
a) ASA congruency
b)SAS congruency
c)SSS congruency
d) Not congruent
Step-by-step explanation:
Step 1:
a)
Angle PRQ = Angle RQS
Angle PRQ = Angle QRS (since PQ is parallel to RS , these form corresponding angles and hence are equal.
QR is the common Side
Hence 2 angles are same and the side which is included are same.Hence the 2 given triangles are congruent.
Step 2 :
b)
Angle IGH = Angle EDF
Side IG = DF and Side GH = DE
Here 2 of the sides of the triangle are same and the Angle which is included are same.
Hence the given triangles are equal
Step 3:
c)
In the given triangles the three sides re equal. Hence as per the side Side Side postulate the triangles are equal.
Step 4:
d) 2 angles are equal but the equal Side is not included and hence the two triangles are not congruent
y = 5x + 15
y = -5x - 15
Answer:
5x + 15 = -5x - 15
10x = -30
x = -3
y = 5(-3) + 15 = -15 + 15 = 0
(-3,0)
Step-by-step explanation:
Determine if the set is the empty set?
{ | < 10 and > 14}
Answer:
{x| x < 10 and x > 14} is an empty set.
there cannot be any intersection between the two ranges that is , x< 10 and x>14.
Step-by-step explanation:
x < 10 and x > 14 will lead to an empty set.
there cannot be any intersection between the two ranges that is , x< 10 and x>14.
Final answer:
The set with condition { | < 10 and > 14} is the empty set, as no elements can satisfy being both less than 10 and greater than 14 simultaneously.
Explanation:
The set being asked about is defined as { | < 10 and > 14}.
To determine if this set is the empty set, interpret the conditions placed upon the members of the set.
The description says that an element must be both less than 10 and greater than 14 at the same time, which is an impossible condition. Since no number can satisfy both conditions simultaneously, no elements can exist within this set, making it the empty set, often denoted by Ø.
Branliest for who explains
Answer:
The cross section would be a square.
Step-by-step explanation:
The 2 ends of the rectangular prism are squares while the other 4 sides are rectangles. A cross section would be perpendicular to the rectangles, making the cross section a square. The cross section would be parallel to the end squares.
HELP ME I ONLY HAVE 38 MINUTES LEFT I NEED TO GET THIS QUESTION DONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A NUMBER OF Y Increased Increased BY 4 AND ITS AT LEAST IS 25
Answer:
y + 4 ≥ 25
if y is increased by 4 and is at least 25
Sarah has seven apples. Jace has three times as many apples as Sarah. How many apples does Jace have?
Answer:
21
Step-by-step explanation:
7x3=21
Answer:21
Step-by-step explanation:
You can get it srry if that was mean
X Y
3 −2
6 −4
9 −6
12 −8
Determine whether the table represents a proportional relationship. If a proportional relationship exists, what is the constant ratio of y/x
A) yes; − [tex]\frac{2}{3}[/tex]
B) yes; − [tex]\frac{5}{3}[/tex]
C) yes; − [tex]\frac{2}{5}[/tex]
D) The table does not represent a proportional relationship.
Step-by-step explanation:
The given table:
X Y
3 − 2
6 − 4
9 − 6
12 − 8
To find, the constant ratio, [tex]\dfrac{y}{x}[/tex] = ?
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-2}{3}[/tex],
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-4}{6}[/tex] = [tex]\dfrac{-2}{3}[/tex],
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex] and
The constant ratio, [tex]\dfrac{y}{x}[/tex] = [tex]\dfrac{-6}{9}[/tex] = [tex]\dfrac{-2}{3}[/tex]
Thus, the required option A) yes; [tex]\dfrac{-2}{3}[/tex] is correct.
Simplify this please
let's firstly convert the mixed fractions to improper fractions and then multiply.
[tex]\bf \stackrel{mixed}{5\frac{3}{7}}\implies \cfrac{5\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{38}{7}}~\hfill \stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{38}{7}\cdot \cfrac{16}{7}\implies \cfrac{(38)(16)}{(7)(7)}\implies \cfrac{604}{49}\implies 12\frac{20}{49}[/tex]
On a piece of paper, use a protractor and a ruler to construct △ABC with AB=6 cm , m∠A=80° , and m∠B=50° .
What is AC ?
3 cm
6 cm
9 cm
12 cm
Answer:
The measure of side AC is 6 cm.
Step-by-step explanation:
The information for the triangle ABC are:
AB = 6 cm
m∠A = 80°
m∠B = 50°
The sum of all angles of a triangle is 180°.
Compute the value of m∠C as follows:
m∠A + m∠B + m∠C = 180°
m∠C = 180° - 80° - 50°
= 50°
Thus, the angles, m∠C = m∠B.
Consider the triangle below.
If two angles of a triangle are equal or similar then that triangle is known as an isosceles triangle.
And in an isosceles triangle the sides corresponding to the equal angles are equal.
Then in this case as m∠C = m∠B then sides AC = AB.
The measure of the side AC is 6 cm.
There are 52 weeks in a year. Ben has lived in london for two fifths of year. How many weeks has ben lived in london?
Answer:
[tex]\frac{104}{5}[/tex] weeks or [tex]20\frac{4}{5}[/tex] weeks
Step-by-step explanation:
To do this we can set up a proportion
[tex]\frac{52}{1} *\frac{2}{5}[/tex]
This will tell us how many weeks are in 2/5 of a year
Let's evaluate this
[tex]\frac{104}{5}[/tex]
We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below
[tex]20\frac{4}{5}[/tex] weeks
[tex]\text{We're trying to find how many weeks Ben has lived in London}\\\\\text{We know that there are 52 weeks in a year}\\\\\text{We also know that he's been in London for 2/5 of a year, or 40\%}\\\\\text{To find your answer, you could multiply 52 by 0.40}\\\\52*0.40= 20.8\\\\\boxed{\text{Ben has been in London for 20.8 weeks}}[/tex]
The population of a town with an initial population
of 75,000 grows at a rate of 3.7% per year. What
will the population be in 5 years? In 10 years?
Answer:
5 years = 89,940
10 years = 107, 856
Step-by-step explanation:
75000 * 1.037 ^ 5 for the 5 years one
Then do the answer (89940) and times by 1.037 ^ 5. For 10 years
You do it to the power of 5 because you are adding on another 5 years
the\ function\ h\left(x\right)=\frac{1}{2}\left(x+3\right)^{2}+2.How\ is\ the\ graph\ of\ h\left(x\right)\ t\ r\ a\ nslated\ \ from\ the\ parent\ graph\ of\ a\ quadratic\ function,\ f\left(x\right)=x^{2}
The function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.
Explanation:
The parent function is [tex]f(x)=x^{2}[/tex]
The translated function is [tex]h(x)=\frac{1}{2}(x+3)^{2}+2[/tex]
By using the function transformation rules, the translated function h(x) is stretched vertically by a factor of [tex]\frac{1}{2}[/tex]
Also, from the function transformation rules, we know that, [tex]$f(x+b)$[/tex] shifts the function b units to the left.
Thus, the translated function h(x) is shifted 3 units to the left.
By using the function transformation rules, we know that, [tex]$f(x)+b$[/tex] shifts the function b units upward.
Thus, the translated function h(x) is shifted 2 units upwards.
Thus, the translated function h(x) is vertically stretched by a factor of [tex]\frac{1}{2}[/tex] and is shifted 3 units to the left and shifted 2 units up.
melinda used 8 cups of sugar when baking cookies for valentines day. Each bath of cookies used 2/9 cup of sugar. Approximately how many batches of cookies did melinda make for valentines day?
Answer:
36 batches
Step-by-step explanation:
we know that
Each bath of cookies used 2/9 cup of sugar
so
using proportion
Find out how many batches of cookies Melinda makes for 8 cups of sugar
[tex]\frac{1}{(2/9)}\ \frac{bath}{cups}=\frac{x}{8}\ \frac{bath}{cups}\\\\x=8/(2/9)\\\\x=36\ batches[/tex]
wich function represents exponential growth with a growth with a 5% rate of change?
a- f(x) = 4(5)n
b- f(x) = 4(1.05)n
c- f(x)= 4(0.95)n
d- f(x)= 4(0.05)n
Answer:the answer is B
Step-by-step explanation:
The function that represents the exponential growth is
f(x) = 4 x [tex]1.05^n[/tex].
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
An exponential growth function.
Rate of change = 5%
This means,
There is a growth per year of 5%.
The function can be represented as,
f(x) = a [tex](1 +0.05)^n[/tex]
f(x) = a x [tex]1.05^n[/tex]
Where 100% = 1 and 5% = 0.05
Let a = 4
f(x) = 4 x [tex]1.05^n[/tex]
Thus,
The exponential growth function is
f(x) = 4 x [tex]1.05^n[/tex]
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The sum of two numbers is 92. The difference of two numbers is 24. What are the numbers?
Answer:
a = 58
b = 34
Step-by-step explanation:
a + b = 92
a - b = 24
add
a + b + a - b = 92 + 24
2a = 116
a = 116 : 2
a = 58
b = 92 - 58
b = 34
Answer:
Step-by-step explanation:
Let the numbers be x and y
x + y = 92..........(1)
x - y = 24..........(2)
Adding (1) and (2)
2x = 116
x = 116/2
x = 58
From (1)... x + y = 92
58 + y = 92
y = 92 - 58
y = 34
BRIA is a rectangle. AN=5. NR=x-3. please solve for x, NR, and BI
Answer:
x=8
NR=5 units
BI=10 units
Step-by-step explanation:
In a rectangle BRIA
AN=5 units
NR=x-3
We have to solve for x , NR and BI.
We know that
Diagonals of rectangle bisect to each other.
BI and AR are the diagonals of rectangle BRIA and intersect at point N.
AN=NR
[tex]5=x-3[/tex]
[tex]x=5+3=8[/tex]
[tex]x=8[/tex]
Substitute the value of x
NR=8-3=5
By property of rectangle
BI=AR=AN+NR=5+5=10 unit
BI=10 units
Help me plz on this attachment. Ill give Brainly Award comments thanks and high ratings! 2 questions.
Answer:
C. and A.
Step-by-step explanation:
4. 5(x + 3) - 2x
5x + 15 - 2x
3x + 15
5. -6x + 2.5(x - 1) - 5x
-6x + 2.5x - 2.5 - 5x
-8.5x - 2.5
Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.
Answer:
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.
Step-by-step explanation:
Let an exponential growth function is given by [tex]f(x) = a(b)^{x}[/tex]
So, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex], [tex]f(x) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex]
Therefore, this series of values corresponding to the x-value 1, 2, 3, and 4 are in G.P. and the common ratio is b.
Now, from the given tables in the options only the second option i.e. a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16 satisfies an exponential function.
Since, f(1) = 2, f(2) = 4, f(3) = 8 and f(4) = 16 are in G.P.(Answer)
Answer:
2
Step-by-step explanation:
The area of a circle is 28.26 square kilometers. What is the circles diameter
Answer:
6km
Step-by-step explanation:
Area of circle = πr²
Where r = radius, π= 3.14, A = 28.26km²
A = 3.14 x r²
3.14 r2 = 28.26
Divide both sides by 3.14
r²= 28.26/3.14
r² = 9
Square root both sides
r= √9
r= 3
Radius = 3km
Note : Diameter = 2 x radius
Diameter = 3 x 2
Diameter = 6km
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Which function is a shrink of the exponential growth function shown on the graph?
a. f(x) = 2(3)x
b. f(x) = One-half(3)x
c. f(x) = 2(one-third) Superscript x
d. f(x) = One-half (one-third) Superscript x
Answer:
Option B
Step-by-step explanation:
The function in the graph is an exponential growth function.
Therefore its equation is [tex]g(x)=3^x[/tex]
A transformation that shrinks this graph is of the form: [tex]f(x)=k*3^x[/tex] where [tex]0\:<\:k\:<\:1[/tex]
From the given options, we must have [tex]k=\frac{1}{2}[/tex]
This implies that:
[tex]f(x)=\frac{1}{2} (3)^x[/tex]
Answer:
B
Step-by-step explanation:
the temper ire of chicken soup is 192.7 F as it cools the temperature of the soup decreases 2.3 what is the temperature of the soup after 25 minutes
Final answer:
To find the new temperature of the soup after cooling for 25 minutes, multiply the rate of decrease, 2.3 F/min, by 25 minutes to find the total decrease in temperature, which is 57.5 F. Then subtract this from the initial temperature of 192.7 F to get the final temperature of 135.2 F.
Explanation:
The question is about calculating the new temperature of chicken soup after it cools for a certain period. The initial temperature of the soup is 192.7 F, and it's stated that the soup temperature decreases by 2.3 degrees per minute. Since it's asking for the temperature after 25 minutes, we need to multiply the rate of cooling by the number of minutes.
To calculate the new temperature:
Decrease in temperature = 2.3 F/min × 25 min = 57.5 F
The new temperature would then be:
Initial temperature - Decrease in temperature = 192.7 F - 57.5 F = 135.2 F.
Problem Solving Strategies for the Effects of Heat Transfer
Although the question does not require complex problem-solving strategies involving specific heat capacity or mass of the substance, it does simulate a simplified version of heat transfer where we only consider the overall change in temperature over time.
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?
Answer:
$8.60
Step-by-step explanation:
Answer:
$8.60
Step-by-step explanation:
Find the number of shaded triangles for each
figure.
First triangle:
Second triangle
Third triangle
Fourth triangle:
Answer:
1st triangle = 1
2nd triange= 3
3rd triangle = 9
4th triangle = 27
A triangle exists a three-sided polygon with three vertices and three edges. The number of triangles in the given figure exists 1, 3, 9, and 27.
What is a triangle?A triangle exists a three-sided polygon with three vertices and three edges. It exists one of the major fundamental geometric forms.
The number of shaded triangles in each of the triangles exists shown below, thus, the number of triangles in each triangle can are:
1st triangle = 1
2nd triangle = 3
3rd triangle = 9
4th triangle = 27
Therefore, the number of triangles in the given figure exists 1, 3, 9, and 27.
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Will make brainliest if answer correctly
Answer:
D
Step-by-step explanation:
When Y is a function of X, the graph is a v shape.
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
The volunteers gave 1368 fliers in total.
Step-by-step explanation:
Given,
Fliers given by volunteers in first neighborhood = [tex]\frac{21}{38}[/tex]
Remaining fliers = 612
Fraction of remaining fliers = [tex]1-\frac{21}{38}=\frac{38-21}{38}[/tex]
Fraction of remaining fliers = [tex]\frac{17}{38}[/tex]
Let,
x be the total fliers given by volunteers.
[tex]\frac{17}{38}\ of\ x=612[/tex]
[tex]\frac{17}{38}x=612[/tex]
Multiplying both sides by [tex]\frac{38}{17}[/tex]
[tex]\frac{38}{17}*\frac{17}{38}x=612*\frac{38}{17}\\\\x=\frac{23256}{17}\\\\x=1368[/tex]
The volunteers gave 1368 fliers in total.
Keywords: fraction, division
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What would be the area?
Total area is 102.3 yd²
Step-by-step explanation:
Step 1:Total area = area of the parallelogram + area of the right triangle
Step 2:Calculate the area of the parallelogram.
Base = 11 yd, Height = 6.2 yd
⇒ Area of the parallelogram = Base × Height = 11 × 6.2 = 68.2 yd²
Step 3:Calculate the area of the right triangle.
Height = 6.2 yd, Base = 11 yd (Since opposite sides of a parallelogram are equal)
⇒ Area of the triangle = 1/2 × base × height = 1/2 × 11 × 6.2 = 34.1 yd²
Step 4:Calculate the total area.
⇒ Total area = 68.2 + 34.1 = 102.3 yd²
Compute 5e2 - 4g + 7 where e = 4 and g = 6 ?
The value of expression is 63 when e = 4 and g = 6
Solution:
Given expression is:
[tex]5e^2-4g+7[/tex]
We have to solve the expression
Given that e = 4 and g = 6
Substitute e = 4 and g = 6 in given expression
[tex]\rightarrow 5(4)^2 -4(6) + 7\\\\Simplify\ the\ above\ equation\\\\\rightarrow 5(16) -24 + 7\\\\\rightarrow 80-24+7\\\\Simplify\\\\\rightarrow 56+7=63[/tex]
Thus value of expression is 63