Answer:
Answer is A (-3p^8/4q^3)
Step-by-step explanation:
We want to simplify a fraction. The simplification is:
[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{-3*p^8}{4*q^3}[/tex]
So we start with the fraction:
[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}}[/tex]
Where:
p ≠ 0.q ≠ 0.Now, remember the rule:
[tex]\frac{x^n}{x^m} = x^{n - m}[/tex]
Then we can rewrite:
[tex]\frac{15*p^{-4}*q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{15}{-20}*\frac{p^{-4}}{p^{-12}}*\frac{q^{-6}}{q^{-3}} \\\\= -\frac{-3}{4}*p^{-4 - (-12)}*q^{-6 - (-3)}\\\\= -\frac{-3}{4}*p^{8}*q^{-3}\\\\= \frac{-3*p^8}{4*q^3}[/tex]
And we can't keep simplifying this, so this is the correct answer.
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Micheal took his brother to the movies. Micheal paid regular price, but it cost $2 less for his brother at the child price. It cost Micheal $12 total for the movie. How much did it cost for his brother?
It cost $5 for his brother's ticket.
Step-by-step explanation:
Let,
Micheal's ticket price= x
His brother ticket price = y
According to given statement;
x+y=12 Eqn 1
y = x-2 Eqn 2
Putting value of y from Eqn 2 in Eqn 1
[tex]x+(x-2)=12\\x+x-2=12\\2x=12+2\\2x=14\\[/tex]
Dividing both sides by 2;
[tex]\frac{2x}{2}=\frac{14}{2}\\x=7[/tex]
Putting x=7 in Eqn 2
[tex]y=7-2\\y=5[/tex]
It cost $5 for his brother's ticket.
Keywords: linear equation, substitution method
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(?,5) is on the line LaTeX: 4x-7y=14 x − 7 y = 1. Find the other half of the coordinate.
Answer:
The other half of the coordinate is 9
Step-by-step explanation:
Given as :
The points is ( a , 5 )
The line equation is 4 x - 7 y = 1
Now if the given points lies on the given line , then it must satisfy the line equation
So , We have to put the points on the given line
I. e 4 x - 7 y = 1
And the points as ( x , y ) = ( a , 5 )
So , 4 × a - 7 × 5 = 1
Or, 4 a - 35 = 1
or, 4 a = 1 + 35
Or , 4 a = 36
∴ a = [tex]\frac{36}{4}[/tex]
I.e a = 9
So, The value of coordinates as ( a , 5 ) is ( 9 , 5 )
Hence The other half of the coordinate is 9 . Answer
There were 346 tickets purchased for a major league baseball game. The lower reserved tickets cost $9.50 and the upper reserved tickets cost $8.00. The total amount
of money spent was $3224.00. How many of each kind of ticket were purchased?
Answer:
The total number of lower reserved tickets is 304 and
The total number of upper reserved tickets is 42
Step-by-step explanation:
Given as :
The total tickets purchased = 346
The price for lower tickets = $ 9.50
The price for upper tickets = $ 8.00
The total amount spent on tickets = $ 3224
Let the number of lower tickets = L
The number of upper tickets = U
Now, According to question
L + U = 346 ........1
And 9.50 L + 8 U = 3224 ....2
so , 8 ( L + U ) = 346 × 8
or, 8 L + 8 U = 2768
And 9.50 L + 8 U = 3224
Now, solving equation
( 9.50 L + 8 U ) - ( 8 L + 8 U ) = 3224 - 2768
Or, 1.50 L + 0 = 456
Or, L = [tex]\frac{456}{1.50}[/tex]
∴ L = 304
Put the value of L in eq 1
So, L + U = 346
I.e U = 346 - L
Or, U = 346 - 304
∴ U = 42
Hence The total number of lower reserved tickets is 304 and
The total number of upper reserved tickets is 42 . Answer
what's y+24 over 4 equals to 8
Answer:
y = 8
Step-by-step explanation:
8 + 24 = 32
32/4 = 8
Answer:
Step-by-step explanation:
y+24/4=8
y+24=8*4
y+24=32
y=32-24
y=8
Please answer this correctly
Answer:
16 ounces of clay he need.
Step-by-step explanation:
Given:
Reggie had 2-pound bricks of clay and his job is to give 4 ounces of clay to each student.
There are total 28 students.
Now, to get how much ounces of clay does the each student have first we multiply the number of students to the number of ounces of clay.
Number of students × Number of ounces of clay:
[tex]28\times 4[/tex]
[tex]112[/tex]
Now, total amount of clay ounces Reggie had= 3×32=96 ounces. (1 pound = 16 ounces, 2 pound = 32 ounces.)
So, the total amount of clay he need is = [tex]112-96[/tex]
= [tex]16[/tex]
Therefore, 16 ounces of clay he need.
Answer:
Reggie requires 16 Ounces more clay.
Step-by-step explanation:
Given:
Reggie took from shelf 3 of 2 pounds bricks of clay from shelf.
1 pound = 16 ounces
2 pounds = 32 ounces
Total Clay Reggie has in ounces = [tex]3\times 32\ ounces = 96 \ ounces[/tex]
Total Students in his class = 28 students
his job is to distribute 4 ounces of clay to each child
Total number of clay required for whole class in ounces = [tex]28\times4 = 112[/tex]
Remaining Amount of clay requires in ounces = Total number of clay required for whole class in ounces - Total Clay Reggie has in ounces = [tex]112 \ ounces - 96 \ ounces = 16 \ ounces[/tex]
Hence, Reggie requires 16 Ounces more clay to distribute among the whole class
A person whose foot length is 10 inches is 67 inches tall. A human-like creature has a foot length of 35 inches. Use a proportion to find the height of the creature.
Answer:
the creature 268 inches tall
Step-by-step explanation:
set it up and cross multiply!
10 = 40
67 X
67*40=10*X
2680=10X
then divide 10 from both sides:
so X=268
$29,000; 4% decrease
29000 x 0.04 = 1,160
29000 - 1,160 = answer
27,840 = answer
Hope this helps!
Answer:
29,000, percentage decreased by 4% (percent) of its value = 27,840
. Miranda is braiding her hair. Then she will attach
beads to the braid. She wants of the beads to
be red. If the greatest number of beads that will
fit on the braid is 12, what other fractions could
represent the part of the beads that are red?
Answer:
The fractions like [tex](\frac{8}{2}), (\frac{16}{4}), (\frac{44}{11} )[/tex] could represent the part of the beads that are red.
Step-by-step explanation:
The given question is incomplete. Here is the complete question:
Miranda is braiding her hair. Then she will attach beads to the braid, she wants 1/3 of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?
Now, total number of beads to be fit on the braid = 12
The desirable amount of red beads = 1/3
So, now as the number of red beads Miranda can use
= 1/3 ( Total beads used)
= [tex]\frac{1}{3} \times 12 = 4[/tex]
or, out of total 12 beads, 4 beads are red.
⇒The total number of red beads = 4
Hence, the fractions like [tex](\frac{8}{2}), (\frac{16}{4}), (\frac{44}{11} )[/tex] could represent the part of the beads that are red.
Miranda can use fractions with 12 in the denominator to represent the portion of red beads on her braid. Possible fractions include 1/12, 2/12, 3/12, 4/12, 5/12, 6/12, and so on up to 11/12.
Miranda wants 1/12 of the beads to be red on her braid. Since the greatest number of beads that will fit on the braid is 12, the other fractions that could represent the part of the beads that are red must also be fractions with 12 in the denominator to be comparable.
Possible fractions representing red beads out of a total of 12 beads are:
1/12 (one red bead)2/12 (which can be reduced to 1/6)3/12 (which can be reduced to 1/4)4/12 (which can be reduced to 1/3)5/12 (five red beads)6/12 (which can be reduced to 1/2)And so on, up to 11/12 (eleven red beads).These represent all the simple fraction options for the number of red beads based on the constraint of having a maximum of 12 beads.
Bar graphs are useful for showing:
Bar graphs are effective for illustrating and comparing quantitative categories like size, quantity, rates, and distances. The bars can represent different entities and their height indicates a numerical or percentage value. This visual comparison aids in identifying data patterns, trends and relationships.
Explanation:Bar graphs are a useful form of data representation in mathematics, especially when needing to illustrate and compare quantitative categories such as size, quantity, rates, and distances. In these graphs, just as it shows in Figure A7 and Figure A8, the bars can denote different categories like countries or years, and the height of the bars on the vertical axis signifies a numerical or a percentage value. The strength of bar graphs lies in their ability to provide a visual comparison, making it easier to spot patterns, trends, and the relationships between data.
Other types of graphs, such as line graphs and pie charts, have their unique uses, too. A line graph is best for showing the relationship over time between two variables, like the unemployment rate. Pie charts demonstrate how something is divided into parts, such as how a group of people or a sum of money is distributed.
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Finding values or
k(x) = x - 2
h(x) = x2 +1
(h + k)(2) =
Answer:
(h + k)(2) = 5Step-by-step explanation:
[tex](h+k)(x)=h(x)+k(x)\\\\\bold{METHOD\ 1:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(k+h)(2)=h(2)+k(2)\\\\\text{Calculate}\ h(2)\ \text{and}\ k(2).\\\text{Put}\ x=2\ \text{to the equations of the functions}\\\\h(2)=2^2+1=4+1=5\\k(2)=2-2=0\\\\\text\\\\\text{Substitute:}\\\\(h+k)(2)=5+0=5[/tex]
[tex]\bold{METHOD\ 2:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(h+k)(x)=h(x)+k(x)=(x^2+1)+(x-2)=x^2+x-1\\\\(h+k)(2)-\text{put}\ x=2\\\\(h+k)(2)=2^2+2-1=4+2-1=6-1=5[/tex]
There are six times as many whitetail deer as mule deer in the woods. If Jacob gets one deer in the woods? What is the probability that Jacob gets a mule deer?
Answer:
C) The probability that Jacob gets a mule deer is 1/7.
Step-by-step explanation:
Let us assume the number of mule deer in the woods = m
So, the number of whitetail deer = 6 x ( Number of mule deer) = 6 (m) = 6 m
Also, the total number of deer = Mule deer + whitetail deer
= m + 6 m = 7 m
Let E: Event of Picking a mule deer in the woods.
[tex]\textrm{P(E)} = \frac{\textrm{Number of favorable observations}}{\textrm{ Total number of observations }}[/tex]
So, here [tex]\textrm{P(Picking a mule deer )} = \frac{\textrm{Number of Mule deers in the woods}}{\textrm{ Total number of deer }} = \frac{m}{7m} = \frac{1}{7}[/tex]
or, P(E) = 1/7
Hence, the probability that Jacob gets a mule deer is 1/7.
Answer:
C) The probability that Jacob gets a mule deer is 1/7.
Step-by-step explanation:
Let us assume the number of mule deer in the woods = m
So, the number of whitetail deer = 6 x ( Number of mule deer) = 6 (m) = 6 m
Also, the total number of deer = Mule deer + whitetail deer
= m + 6 m = 7 m
Let E: Event of Picking a mule deer in the woods.
So, here
or, P(E) = 1/7
Hence, the probability that Jacob gets a mule deer is 1/7.
Anna has 196 pepper plants that she wants to plant in a square formation how many pepper plants should she plant in each row
She should plant 14 plants in each row
Step-by-step explanation:
Given
Total pepper plants = 196
As the plants have to be in square shape, the number of rows and the plants in each row will be equal
Let x be the number of rows
Then
[tex]x^2 = 196\\[/tex]
Taking square root on both sides
[tex]\sqrt{x^2} = \sqrt{196}\\x = 14[/tex]
Hence,
She should plant 14 plants in each row
Keywords: Square root, Radicals
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What is 3 increased by 50? Decreased by 60? Decreased by 100?
Answer: 53 -10 -50
Step-by-step explanation:
50 + 3 = 53 50 - 60 = -10 50 - 100 = -50
[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]53[/tex].
[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]-57[/tex].
[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]-97[/tex].
To increase a number [tex]a[/tex] by [tex]b[/tex] means to add [tex]a[/tex] to [tex]b[/tex]. Increase is denotes by sign [tex]+[/tex]
To decrease a number [tex]a[/tex] by [tex]b[/tex] means to subtract [tex]b[/tex] from [tex]a[/tex]. Decrease is denoted by sign [tex]-[/tex]
[tex]3[/tex] increased by [tex]50[/tex] is equal to [tex]\boldsymbol{3+50}[/tex] which is equal to [tex]53[/tex].
[tex]3[/tex] decreased by [tex]60[/tex] is equal to [tex]\boldsymbol{3-60}[/tex] which is equal to [tex]-57[/tex].
[tex]3[/tex] decreased by [tex]100[/tex] is equal to [tex]\boldsymbol{3-100}[/tex] which is equal to [tex]-97[/tex].
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Calculate the distance between the points (-1, 3) and (4, -1).
Enter your answer to the tenths place
Distance=_____units
The distance between those two points is 41 and in decimal form to the nearest tenth, that's 6.4
Explanation:
Use the distance formula: √(x2 - x1)² + (y2 - y1)²
Then we plug in our x's and y's:
√(4 - (-1))² + ((-1) - 3)²
Then you simplify:
√(5)² + (-4)² = √25 + 16
√41 (And if you need to, you can put this into decimal form.)
Answer:
6.4
Step-by-step explanation:
Use the distance formula and then fill in points for the variables.
The cycling team is ranked by the total time it takes its team members to
finish the course. The total time for all 3 members is 12 hours. If Susan takes
3 times as long as Gina, and Michael takes 2 times as long as Gina, how
many hours does it take Gina to complete the course?
Answer:2 hrs
Step-by-step explanation:
x+2x+3x=12
6x=12
x=2
Let f(x)=8x and g(x)=8x+5+1 .
Which transformations are needed to transform the graph of f(x) to the graph of g(x) ?
Select each correct answer.
horizontal translation 5 units right
vertical translation 1 unit up
vertical translation 1 unit down
horizontal translation 5 units left
horizontal translation 1 unit left
vertical translation 5 units up
The transformations are needed to transform the graph of f(x) to the graph of g(x) are:
vertical translation 1 unit up ⇒ 2nd answer
horizontal translation 5 units left ⇒ 4th answer
Step-by-step explanation:
Let us revise the translation:
If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k∵ f(x) = 8x
∵ g(x) = (8x + 5) + 1
- From the notes above translation to the left h units added x by h
∵ 8x is added by 5
∴ f(x) translated 5 units to the left
- From the notes above translation up k units added f(x) by k
∵ f(x) is added by 1
∴ f(x) translated 1 unit up
The transformations are needed to transform the graph of f(x) to the graph of g(x) are:
vertical translation 1 unit up
horizontal translation 5 units left
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the answers are
horizontal translation 5 units left
vertical translation 1 unit up
I failed lol :((
I NEED HELP ASAP..
WILL GIVE BRAINLIEST.
50 POINTS!
Answer:
see the explanation
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides
step 1
Find the coordinates of point X (midpoint of segment AC)
we have
A(0,2a), C(2a,0)
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]X(\frac{0+2a}{2},\frac{2a+0}{2})[/tex]
[tex]X(a,a)[/tex]
step 2
Find the length side AX
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(0,2a), X(a,a)
substitute
[tex]AX=\sqrt{(a-2a)^{2}+(a-0)^{2}}[/tex]
[tex]AX=\sqrt{(-a)^{2}+(a)^{2}}[/tex]
[tex]AX=a\sqrt{2}\ units[/tex]
step 3
Find the length side BX
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
B(0,0), X(a,a)
substitute
[tex]BX=\sqrt{(a-0)^{2}+(a-0)^{2}}[/tex]
[tex]BX=\sqrt{(a)^{2}+(a)^{2}}[/tex]
[tex]BX=a\sqrt{2}\ units[/tex]
step 4
Compare the length side AX and BX
[tex]AX=a\sqrt{2}\ units[/tex]
[tex]BX=a\sqrt{2}\ units[/tex]
[tex]AX=BX[/tex]
so
The triangle AXB has two equal sides
therefore
Triangle AXB is an isosceles triangle
Answer:
Soooooooooooooo
Step-by-step explanation:
Okay.... Let me look up how to do this
A box is filled with 2 brown cards,8 yellow cards, and 8 green cards. A card is chosen at random from the box. What is the probability that the card is not yellow?
2 brown, 8 yellow, 8 green, thus our sample space is 2+8+8 = 18.
What is the probability that the card is NOT yellow? How many non-yellow are there? well 2 + 8 = 10, favorable outcomes.
[tex]\bf \cfrac{\stackrel{\textit{favorable outcomes}}{10}}{\underset{\textit{sample space}}{18}}\implies \cfrac{5}{9}\implies 0.\overline{555}\qquad \approx \qquad 55.6\%[/tex]
Which figure shows the correct dimensions of a 2/5 scale drawing of the given figure
To find the correct dimensions of a scaled drawing or the actual dimensions based on a scale factor, multiply the scaled dimensions by the denominator of the scale factor. For a scale factor of 1/200, if a scaled drawing has dimensions of 1 meter by 1 meter, the actual dimensions would be 200 meters by 200 meters, yielding an area of 40,000 square meters.
Explanation:To determine the correct dimensions of a scaled drawing or the actual dimensions based on a scale factor, it is essential to understand the ratio that the scale factor represents. If the scale factor for a drawing is given as 1/200, it signifies that every unit of measurement on the drawing represents 200 of the same units in the actual size.
For example, let's assume you have a scaled drawing with dimensions of 1 meter by 1 meter, and the scale factor is 1/200. To find the actual dimensions, you would multiply the scaled dimensions by the scale factor's denominator:
Actual length = 1 meter imes 200 = 200 metersActual width = 1 meter imes 200 = 200 metersOnce you know the actual dimensions, finding the area involves multiplying the length by the width. Using our example:
Area = Actual length imes Actual widthArea = 200 meters imes 200 meters = 40,000 square metersWhen creating or analyzing scale drawings, remember to apply the scale factor consistently to each dimension to obtain accurate results.
Sonya makes a pattern of values for x and a pattern of values for y. Which
ordered pair continues the patterns and has an x-value of 6?
Answer:
6,9!
Step-by-step explanation:
Goodluck on your I-Ready!
To find the ordered pair with an x-value of 6, we need to look at the pattern for x and find the corresponding value for y. Using the pattern provided, the ordered pair would be (6, 18).
The problem states that Sonya is making a pattern of values for x and a pattern of values for y. We are asked to find the ordered pair that continues the patterns and has an x-value of 6.
To solve this, we need to look at the pattern for the x-values and find the corresponding value for y. Once we have the y-value, we can form the ordered pair (x, y) with x = 6.
For example, let's say the pattern for x is: 1, 2, 3, 4, 5
And the pattern for y is: 3, 6, 9, 12, 15
In this case, we can see that for x = 6, the corresponding y-value would be 18. So the ordered pair would be (6, 18).
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Do the number 7 please I really need it do tomorrow
Answer: y=4, x=-2
Step-by-step explanation:
line r must have the equation y=4 to go through point (-2,4)
line s must have the equation x=-2 to go through point (-2,4)
Cot^2 x- 6cotx - 5=0
Step-by-step explanation:
cotx=t
t^2-6t-5=0
t=cotx=1or5
Solve x2 - 3x = 28 by factoring.
Answer:
x = -4 or x = 7Step-by-step explanation:
[tex]x^2-3x=28\qquad\text{subtract 28 from both sides}\\\\x^2-3x-28=0\\\\x^2+4x-7x-28=0\qquad\text{distribute}\\\\x(x+4)-7(x+4)=0\\\\(x+4)(x-7)=0\iff x+4=0\ \vee\ x-7=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\\boxed{x=-4}\\\\x-7=0\qquad\text{add 7 to both sides}\\\boxed{x=7}[/tex]
Answer:
x = -4 or x = 7
What’s the element?
How many reactants in each?
How many products in each?
Is it balanced?
Explanations and Steps:
How to find the elements:
*Take every element (either one capital letter OR two letters with the first capital and second lowercase)
*Reference the periodic table to find the element name
The number of reactants:
*Reactants are on the left side, what there is before the reaction
*Each reactant is separated by the + sign
*They may be more than one element
The number of products:
*Products are on the right side, what there is after the reaction
*Each product is separated with the + sign
*They may be more than one element
Is it balanced:
Count the number of each element on both sides. It is balanced if both sides have the same number of every element.
*Write out each of the element symbols for each side
*Remember the multiply subscripts (little numbers) by coefficients (big numbers)
Answers:
6.
The elements are:
H - hydrogen
Cl - chlorine
Ca - calcium
O - oxygen
# of reactants: 2
# of products: 2
Is it balanced?
Reactants:
H 4
Cl 2
Ca 1
O 2
Products:
H 2
Cl 2
Ca 1
O 1
It's not balanced because H and O have different numbers of atoms in the reactants and products.
7.
The elements are:
K - potassium
Cl - chlorine
O - oxygen
# of reactants: 1
# of products: 2
Is it balanced?
Reactants:
K 1
Cl 1
O 3
Products:
K 1
Cl 1
O 2
It's not balanced because there are three oxygen atoms for reactants but only two oxygen atoms in the product.
8.
The elements are:
K - potassium
P - phosphorus
O - oxygen
H - hydrogen
Cl - chlorine
# of reactants: 2
# of products: 2
Is it balanced?
Reactants:
K 3
P 1
O 4
H 1
Cl 1
Products:
K 3
P 1
O 4
H 3
Cl 3
It's not balanced because H and Cl have different numbers of atoms.
9.
The elements are:
S - sulphur
O - oxygen
# of reactants: 2
# of products: 1
Is it balanced?
Reactants:
S 2
O 6
Products:
S 2
O 6
It's balanced because both sides have 2 sulphur atoms and six oxygen atoms.
10.
The elements are:
K - potassium
I - iodine
Pb - lead
N - nitrogen
O - oxygen
# of reactants: 2
# of products: 2
Is it balanced?
Reactants:
K 2
I 2
Pb 1
N 2
O 6
Products:
K 1
I 2
Pb 1
N 1
O 3
It's not balanced because K, N and O have different numbers of atoms.
11
Simplify.
5-8 x 54
-
Answer:
-427
Step-by-step explanation:
5-8 x 54
It is a very simple numerical simplification. We have to use the BODMAS rule to determine the value of this simplification. At first, we see that there is no bracket, so we will go to "or." Since there is no "or," we will go to the "divide" rule. Again, there is no "Divide," so we will go to the "Multiplication" rule.
= 5 - (8 x 54)
= 5 - 432
Now, we will deduct 432 from 5. Since 432 is a negative number, the answer will be a negative value.
= -427
The simplification answer = -427
Factor the algebraic expression below in terms of a single trigonometric function. cos x - sin^2 x - 1
please help me, ive been struggling so hard. make it easy to follow along? i found it answered on here but it confused me. idk
Answer:
(cosx + 2)(cosx - 1)
Step-by-step explanation:
Using the trigonometric identity
cos²x + sin²x = 1 ⇒ sin²x = 1 - cos²x
Given
cosx - sin²x - 1
= cosx - (1 - cos²x) - 1
= cosx - 1 + cos²x - 1
= cos²x + cosx - 2
= (cosx + 2)(cosx - 1) ← in factored form
The Sale amount 399.79 and the sales tax is 5% what is the total amount paid
Final answer:
After rounding to the nearest cent, the total payable sum is $419.78.
Explanation:
To calculate the total amount paid for an item with a sales tax, you first need to find the amount of sales tax by converting the tax rate from a percentage into a decimal. In this case, the sale amount is $399.79 and the sales tax is 5%.
Convert the percent to a decimal by dividing by 100:
5% ÷ 100 = 0.05
Next, multiply the sale amount by the decimal tax rate to find the amount of sales tax:
$399.79 × 0.05 = $19.9895
Since we usually round money to the nearest cent, round $19.9895 to $19.99.
Finally, add the amount of sales tax to the original sale amount to find the total amount paid:
$399.79 + $19.99 = $419.78
Therefore, the total amount paid including sales tax is $419.78.
There are 235 seventh-grade students going on a field trip. The school has 5 buses to take the students. Each bus has 22 seats, and 2 students can sit in each seat. Based on this information, how many students will not be able to ride on a bus for the field trip?
15 students will not be able to ride on bus for the field trip.
Step-by-step explanation:
No. of seats in one bus = 22 seats
1 seat is for 2 students, therefore, one bus can sit students;
No. of students in one bus = 22*2 = 44 seats
Total buses = 5
One bus can have 44 students, 5 buses can have;
5 buses = 44*5 = 220 students
Total students = 235
As the buses can have 220 students;
Students left = Total students - No. of students in 5 buses
[tex]Students\ left=235-220=15\ students[/tex]
15 students will not be able to ride on bus for the field trip.
Keywords: multiplication, subtraction
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Final answer:
There are 15 seventh-grade students who will not be able to ride on a bus for the field trip, as the total bus seating capacity is for 220 students and there are 235 students going on the trip.
Explanation:
The subject of this question is Mathematics, specifically a problem involving division and subtraction to determine the number of students who will not have a seat on the buses. To solve this, we need to calculate the total seating capacity of all buses and then find the difference between the number of students and the total seating capacity.
Each bus has 22 seats and each seat can accommodate 2 students, so each bus can carry 22 x 2 = 44 students. There are 5 buses, so the total seating capacity is 5 x 44 = 220 students.
There are 235 seventh-grade students going on the field trip. To find out how many will not be able to ride the bus, we subtract the total seating capacity from the number of students: 235 - 220 = 15 students will not be able to ride on a bus for the field trip.
use figure 8.1. Corey Griffin obtained an installment loan of $1000. The annual percentage rate is 8 percent. He must repay the loan in 18 months. What is the finance charge?
A. $63.80
B. $75.10
C. $70.00
D. $78.20
Answer:
Option A. $63.80
Explanation:
The figure contains a table with the monthly payment on a a $100 loan in function of the number of months (term in months) and the annual percent rates (8.00%, 10.00%, 12.00%, 14.00%).
You find the monthly payment on an $100 loan for the terms of the installment loan obtained by Corey Griffin, in the cell resulting from the intersection of the row for 18 months and the column for the rate of 8.00%. That is 5.91.
The meaning of that value is that it must repaid $5.91 monthly, per each $100 of loan.
Hence, for the $1,000, you compute the monthly payment in this way:
Monthly payment = $1,000 × ( $5.91 / $100) = $59.10Now, to find the finance charge, compute the total payments and subtract the amount of the loan:
Total payments = 18 months × $59.10 / month = $1,063.80Finance charge = Total payments - loan amount = $1,063.80 - $1,000 = $63.80Thus, the finance charge is $63.80 (option A).
The length of a rectangle is 8 more than twice it’s width. The perimeter is 96 feet. Find the dimensions of the rectangle
Answer:
width is 12 feet. Length is 32 feet.
Step-by-step explanation:
Answer:
Length= 52 Width= 44
Step-by-step explanation: