There are two ways to evaluate the expression:
32(16 - 6)
WAY 1
Evaluate the expression in the bracket first, then multiply the result by the content outside the bracket.
32(10)
= 320
WAY 2
Remove the bracket straight, without simplifying the content inside the bracket by multiplying 32 by each element in the bracket.
32*16 - 32*6
= 512 - 192
= 320
And those are the two ways.
Which angles are adjacent and do NOT form a linear pair?
Adjacent angles share a common side and a common vertex but do not overlap each other.
A linear pair is two adjacent angles that creat a straight line, thus adjacent angles which do not form a linear pair could be:
[tex]\angle2\text{ and }\angle3[/tex]If there are 40 seats per row how many seats are in 90 rows?
Answer:
3,600 seats
Step-by-step explanation:
If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.
-Hope this helps
Answer:
Step-by-step explanation:
3600
If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
Given that angle A lies in Quadrant I and sin(A)= 30/31, evaluate cos(A)
Which function has a y-intercept of 4? a. f(x) = 3(1 + 0.05)* b.f(x) = 4(0.95)* c. f(x) = 5(1.1) d. f(x) = 5(0.8)
Answer:
The correct option is D
f(x) = 5(0.8)
has y-intercept of 4
Explanation:
To know which of the given functions has a y-intercept of 4, we test them one after the other.
a. f(x) = 3(1 + 0.05)
f(x) = 3.15 WRONG
b. f(x) = 4(0.95)
f(x) = 3.8 WRONG
c. f(x) = 5(1.1)
f(x) = 5.5 WRONG
d. f(x) = 5(0.8)
f(x) = 4 CORRECT
Which of the followingrepresents this inequality?|4x – 61 > 10
Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42 – 3x. Find and interpret the x- and y-intercepts.
Answer:
y-intercept: 42
x-intercept: 14
Step-by-step explanation:
The y-intercept can be found with the given equation:
y = 42 - 3x
Either Let x = 0 to find the y-intercept. OR,
rearrange the equation to y=mx+b to see the y-intercept, which is b in the equation.
y = 3(0) + 42
y = 42
The y-intercept is 42 and this means that the original, uncut length of the string (zero cuts) is 42.
To find the x-intercept, let y = 0.
y = 42 - 3x
0 = 42 - 3x
Add 3x to both sides.
3x = 42
Divide by 3.
x = 42/3
x = 14
An x-intercept of 14, means that at 14 cuts there will be no more string left. The length of the string is now 0.
Hi can you help me find the correct match to each question?
GIVEN:
We are given a set of 4 statements as indicated in the attached image.
Required;
Determine whether each statement is TRUE or FALSE.
Solution;
(1) Look at the digit to the right of the digit to which you are rounding to tell whether to round up or leave it the same.
This statement is TRUE
(2) If the digit to the right of the digit to which you are rounding is four or less, you keep the digit the same.
This statement is TRUE.
(3) If the digit to the right of the digit to which you are rounding is five or more, you keep the digit the same.
This statement is FALSE.
(4) Look at the digit to the left of the digit to which you are rounding to tell whether to round down or leave it the same.
This statement is FALSE.
sandy made 8 friendship bracelets. she gave 1/8 to her best friend and 5/8 to her friends on the tennis team. write and solve an equation to find the fraction of her bracelets, b , sandy gave away1
Answer:
(3/4)b
Explanation:
• Fraction given to her best friend = 1/8
,• Fraction given to her friends on the tennis team = 5/8
To calculate the total proportion of the bracelet she gave away, we add:
[tex]\begin{gathered} (\frac{1}{8}+\frac{5}{8})b \\ =\frac{6}{8}b \\ =\frac{3\times2}{4\times2}b \end{gathered}[/tex]Reducing the fraction to its lowest form by canceling out 2 gives:
[tex]=\frac{3}{4}b[/tex]Casey's Cookie Company opened with 24 cupcakes in the store display case. By noon, therewere only 15 cupcakes left. Was there a percent increase or decrease in the amount ofcupcakes? What was the increase or decrease amount?
Percentage is the proportion between numbers
total initial of cakes for Casey's = 24
final number of cakes = 15
find proportion 15/24 how many represents
15/24 = 5/8
now divide 100/8 = 12.5
then multiply 12.5 x 5
12.5x5= 62.5 %
Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
The breakeven point of Angel Corporation equals to 11,500 units.
How do we get the breakeven point?Given that the unit price is $25.99, so if they sell a x units, then, the revenue is: R(x) = $25.99*x
Given that the cost per unit is $18.95, plus a fixed cost of $80,960, then, the cost of x units is: C(x) = $80,960 + $18.95*x
Now, the breakeven point is a value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/$7.04
x = 11,500 units
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Can someone help me with this please and thank you
The histogram is skewed to the left, the mean is less than the median.
Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbA bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(red, then blue).
5 + 6 + 4 = 15
red is 6/15 then taken out
then blue is 5/14
6/15 * 5/14 = 1/7
1/7 or about 0.143
Carl Heinrich had lateral filing cabinets that need to be placed along one wall of a storage closet. The filing cabinets are each 2 1/2 feet wide and the wall is 15 feet long. Decide how many cabinets can be placed along the wall
In this case we have to divide the length of the wall by the width of a cabinet. Doing so, we have:
[tex]\begin{gathered} 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}\text{ (Converting the mixed number to an improper fraction)} \\ \frac{15}{1}\div\frac{5}{2}=\frac{15\cdot2}{5}(\text{Dividing fractions)} \\ \frac{15\cdot2}{5}=\frac{30}{5}=6\text{ (Simplifying the result)} \\ \text{The answer is 6 cabinets.} \end{gathered}[/tex]An architect is designing the roof for a house what is the height of the roof?
An architect is designing the roof for a house
what is the height of the roof?
From the diagram,
We have that tan 30 = h/ 12
0.5774 = h/ 12
cross-multiply,
h = 12 x 0.5774
h = 6.9288 feet
If the revenue function for a certain item is R(x)=20x−0.25x2, what is the marginal revenue for the 8th item? Do not include the dollar sign in your answer.
The marginal revenue of the 8th item from the revenue function is 16
How to determine the marginal revenue?From the question, the revenue function is given as
R(x) = 20x - 0.25x^2
To calculate the marginal revenue, we start by differentiating the revenue function
This is calculated as follows
R(x) = 20x - 0.25x^2
Differentiate the function
R'(x) = 20 - 0.5x
The above represents the marginal revenue function
So, we have
M(x) = 20 - 0.5x
For the 8th item, we have
M(8) = 20 - 0.5 x 8
Evaluate
M(8) = 20 - 4
Evaluate
M(8) = 16
Hence, the marginal revenue is 16
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If the price of gas was on average $2.85 per gallon, and thus was $1.36 cheaper than a year before, what is the percent of decrease in price?
The price of gas = $2.85 per gallon
It was $1.36 cheaper than a year before.
So, the price before = 2.85 + 1.36 = $4.21
So, the percent of decrease = 1.36/4.21 = 0.323 = 32.3%
Solve for y: 5 left parenthesis 3 y plus 4 right parenthesis equals 6 open parentheses 2 y minus 2 over 3 close parentheses The solution is Y = _______
ANSWER:
-8
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]5\cdot\mleft(3y+4\mright)=6\cdot\mleft(2y-\frac{2}{3}\mright)[/tex]Solving for y:
[tex]\begin{gathered} 15y+20=12y-4 \\ 15y-12y=-4-20 \\ 3y=-24 \\ y=-\frac{24}{3} \\ y=-8 \end{gathered}[/tex]The solution of y is equal to -8
Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 − 2x2 − 15x
x =
Answer:
-3, 0, 5
Step-by-step explanation:
You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.
Factored formWe notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:
P(x) = x(x² -2x -15)
To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...
P(x) = x(x +3)(x -5) . . . . factored form
ZerosThis product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...
x = 0
x +3 = 0 ⇒ x = -3
x -5 = 0 ⇒ x = 5
The zeros of P(x) are -3, 0, 5.
What is the probability that a meal will include a hamburger
ANSWER:
The probability that a meal will include a hamburger is 25%
SOLUTION:
The total combination of one entree and one drink is 4* 2 = 8
The total combination of one hamburger meal is 1*2 = 2
The probability is 2/8 or 1/4 or 25%
Perform the indicated operation of multiplication or division on the rational expression and simplify
The division of two fractions is the same as multiplying the first by the inverted second fraction:
Then, in this case:
[tex]\frac{24y^2}{5x^2}\div\frac{6y^3}{25x^2}=\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}[/tex]Step 2: multiplication of two fractionsWe multiply two fractions by multiplying the numerators and the denominators:
[tex]\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}=\frac{24y^2\times25x^2}{5x^2\times6y^3}[/tex]Step 3: simplifying the numbers of the fractionWe know that
[tex]\frac{25}{5}=5\text{ and }\frac{24}{6}=4[/tex]Then, we can use this in our fraction:
[tex]\begin{gathered} \frac{24y^2\times25x^2}{5x^2\times6y^3}=5\cdot4\frac{y^2x^2}{x^2y^3} \\ \downarrow\text{ since 5}\cdot4=20 \\ 5\cdot4\frac{y^2x^2}{x^2y^3}=20\frac{y^2x^2}{x^2y^3} \end{gathered}[/tex]Step 4: exponents of the resultWe know that if we have a division of same base expressions (same letters), the exponent is just a substraction:
[tex]\begin{gathered} \frac{y^2}{y^3}=y^{2-3}=y^{-1} \\ \frac{x^2}{x^2}=x^{2-2}=x^0=1 \end{gathered}[/tex]Then,
[tex]20\frac{y^2x^2}{x^2y^3}=20y^{-1}\cdot1=20y^{-1}[/tex]Since negative exponents correspond to a division, then we can express the answer in two different ways:
[tex]20y^{-1}=\frac{20}{y}[/tex]Answer:[tex]20y^{-1}=\frac{20}{y}[/tex]Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
pls show how did u solve it
Linear function f(x) = 2/7x - 2
It has no domain or range restrictions, so both of them include all real numbers.
Doman x ∈ ( - ∞, + ∞),Range y ∈ ( - ∞, + ∞).The graph is attached
2/___=4/18What is the answer to the problem
Explanation:
These are equivalent fractions, we have to find the missing denominator from the fraction on the left. Since the numerator of the fraction on the right is 4 and the numerator of the fraction on the left is 2, we can see that we have to divide by 2. Therefore 18 divided by 2 is 9. This is the numerat
Answer:
Solve the triangle for the missing sides and angles. Round all side lengths to the nearest hundredth. (Triangle not to scale.)
The Law of Cosines
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]The triangle shown in the figure has two side lengths of a=4 and b=5. The included angle between them is x=100°. We can find the side length c by substituting the given values in the formula:
[tex]c^2=4^2+5^2-2\cdot4\cdot5\cos 100^o[/tex]Calculating:
[tex]c^2=16+25-40\cdot(-0.17365)[/tex][tex]\begin{gathered} c^2=47.946 \\ c=\sqrt[]{47.946}=6.92 \end{gathered}[/tex]Now we can apply the law of the sines:
[tex]\frac{4}{\sin A}=\frac{5}{\sin B}=\frac{c}{\sin 100^o}[/tex]Combining the first and the last part of the expression above:
[tex]\begin{gathered} \frac{4}{\sin A}=\frac{c}{\sin100^o} \\ \text{Solving for sin A:} \\ \sin A=\frac{4\sin100^o}{c} \end{gathered}[/tex]Substituting the known values:
[tex]\begin{gathered} \sin A=0.57 \\ A=\arcsin 0.57=34.7^o \end{gathered}[/tex]The last angle can be ob
Determine the system of inequalities that represents the shaded area .
For the upper line:
[tex]\begin{gathered} (x1,y1)=(0,2) \\ (x2,y2)=(2,3) \\ m=\frac{y2-y1}{x2-x1}=\frac{3-2}{2-0}=\frac{1}{2} \\ \text{ using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-2=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]For the lower line:
[tex]\begin{gathered} (x1,y1)=(0,-3) \\ (x2,y2)=(2,-2) \\ m=\frac{-2-(-3)}{2}=\frac{1}{2} \\ \text{ Using the point-slope equation:} \\ y-y1=m(x-x1) \\ y-(-3)=\frac{1}{2}(x-0) \\ y+3=\frac{1}{2}x \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]Therefore, the system of inequalities is given by:
[tex]\begin{gathered} y\le\frac{1}{2}x+2 \\ y\ge\frac{1}{2}x-3 \end{gathered}[/tex]Find the surface area. Do not round please Formula: SA= p * h + 2 * b
The shape in the question has two hexagonal faces,
The Area of each of the heaxagonal faces is
[tex]=42\text{ square units}[/tex]The shape also has 6 rectangular faces with dimensions of
[tex]8.2\times4[/tex]The area of a rectangle is gotten with the formula below
[tex]\text{Area}=l\times b[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Area}=l\times b \\ \text{Area}=8.2\times4 \\ \text{Area}=32.8\text{square units} \end{gathered}[/tex]To calculate The total surface area of the shape, we will add up the areas of the hexagonal faces and the rectangular faces
[tex]\text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Surface area=}2\times(area\text{ of hexagonal faces)+ 6(area of rectangular faces)} \\ \text{Surface area}=(2\times42)+(6\times32.8) \\ \text{Surface area}=84+196.8 \\ \text{Surface area}=280.8\text{ square units} \end{gathered}[/tex]Hence,
The Surface Area is = 280.8 square units
Riley has $955 in a savings account that earns 15% interest, compounded annually.To the nearest cent, how much interest will she earn in 2 years?
In order to calculate the interest generated in 2 years, we can use the formula below:
[tex]I=P((1+r)^t-1)[/tex]Where I is the interest generated after t years, P is the principal (initial amount) and r is the interest rate.
So, for P = 955, r = 0.15 and t = 2, we have:
[tex]\begin{gathered} I=955((1+0.15)^2-1) \\ I=955(1.15^2-1) \\ I=955(1.3225-1) \\ I=955\cdot0.3225 \\ I=307.99 \end{gathered}[/tex]Therefore the interest generated is $307.99.
In a recent survey of dog owners, it was found that 901, or 34%, of the owners take their dogs on vacation with them. Find the number of dog owners in the survey that do NOT take their dog on vacation with them rounded to the nearest whole number
we have that
34% represents 901 owners that take their dogs on vacation with them
so
the percentage of dog owners in the survey that do NOT take their dog on vacation is equal to
100%-34%=66%
Applying proportion
901/34=x/66
solve for x
x=(901/34)*66
x=1,749 ownersThe point P is on the unit circle. If the y-coordinate of P is −3/5, and P is in quadrant IV, then
x = _________
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],
so x can be positive or negative 4/5,
and we know that x coordinate of any point in quadrant IV is positive,
so x = 4/5.