ANSWER:
Circumference of the circle is 25.12 centimeters
Area of the circle is 50.24 square centimeters
STEP-BY-STEP EXPLANATION:
We have that the formula for the circumference and the area are the following:
[tex]\begin{gathered} c=2\cdot\pi\cdot r \\ A=\pi\cdot r^2 \end{gathered}[/tex]The radius is equivalent to half the diameter, therefore, we replace:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{ replacing} \\ c=2\cdot3.14\cdot4=25.12\text{ cm} \\ A=3.14\cdot4^2=50.24cm^2 \end{gathered}[/tex]the circumference of the circle is 25.12 cm and the area is equal to 50.24 square centimeters
A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze, and the second brand is 55% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?
36 gallons of the 55% brand and 24 gallons of the 30% brand of antifreeze must be used.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let x denote the amount of 30% pure antifreeze required in the combination.
The quantity of the 55% brand is then calculated (60-x).
The pure antifreeze content of the combination as:
⇒ 0.30x +0.30(60 -x) = 0.45 (60)
When we subtract 0.30(60), we get
x(0.55 -0.30) = 60(0.45 -0.30)
To simplify, divide by the coefficient
x = 9/0.25 = 36 .
Therefore, 36 gallons of the 55% brand and 24 gallons of the 30% brand of antifreeze must be used.
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equations with variables4w + 3 = 2w + 7
w = 2
Given 4w + 3 = 2w + 7
Collect like terms
4w - 2w = -3 + 7
2w = 4
Divide both sides by 2
2w/2 = 4/2
w = 2
(a) Latoya's test score average Increased by 8 points this semester.Write a signed number to represent this change in average.(b) Isabel lost 70 dollars from her pocket.Write a signed number to represent this change.
Solution
a) Latoya's test score average Increased by 8 points this semester.
This simply means there is an increase of 8 points in Latoya's test score average.
Thus, a signed number that represents this change in average is +8 points
b) Isabel lost 70 dollars from her pocket.
This simply means there is a decrease in the money in Isabel's pocket.
Thus, a signed number to represent this change is -70 dollars
Find an equivalent expression without parentheses -(6-n)=
Given the expression;
[tex]-(6-n)[/tex]Step 1: We multiply the expression in the parentheses by -1, we have;
[tex]\begin{gathered} =-1(6)-1(-n)_{} \\ =-6+n \end{gathered}[/tex]Hence, -(6-n)= -6+n
What is 3/8 x 3/8 x 3/8 written as a power
Answer:
3/8^3
Step-by-step explanation:
its like 1/2 x 1/2 x1/2 its 1/2^3
or 7x7x7x7x7=7^5 its the same concept....
A walking trail is 3.8 miles long. If Gertrude walked the length of the walking trail 15 times, how many miles did Gertrude walk?
Explanation:
If Gertrude walked the length of the walking trail 15 times, it means that she walked 3.8 miles 15 times. Therefore to find the total distance we have to multiply the length by the times she walked the trail:
[tex]3.8\times15=57[/tex]Answer:
Gertrude walked 57 miles
A piece of cord 1.8 m long is cut evenly into smaller pieces of 0.05 m each. How many of these pieces can be cut?Number of pieces =
Solution:
We are given that :-
• A Piece of a cord = 1.8m long
,• need to cut into smaller pieces of 0.05m each
,• let ",n", be the number of smaller pieces to be cut
0.05 * n = 1.8
∴ n = 1.8/0.05
n = 36
• This means that 36 smaller pieces will be cut into 0.05m
Find the simple interest and the future value for principal amount $110, rate 6%, and time 2 years, The simple interest is $ The future value is $
p = $110
r = 6% = 6/100
t = 2 years
[tex]SI=\frac{prt}{100}=\frac{110\times6\times2}{100}=\frac{1320}{100}=\text{ \$}13.2[/tex]simple interest = $13.2
The future value will be
[tex]\begin{gathered} FV=110(1+0.06)^2 \\ FV=110(1.06)^2 \\ FV=110\times1.1236 \\ FV=123.596=\text{ \$123.596} \end{gathered}[/tex]Davis make 720 a week he has spent 217 what fraction of his week pay has he spent.
Answer:
217/720
Explanation:
• The amount Davis makes in a week = $720
,• The amount he has spent = $217
,•
To determine the fraction of his week's pay that he has spent, divide the amount spent by the amount he makes weekly. That is:
[tex]\frac{217}{720}[/tex]Davis has spent 217/720 of his week's pay.
What's the length of PS, QS, and area of PQR?
First, notice the following right triangle that we can get with the vertices Q,S and P:
then, we can find PS and QS using the trigonometric functions sine and cosine:
[tex]\begin{gathered} \sin (62.58)=\frac{\text{opposite side}}{hypotenuse}=\frac{PS}{4.5} \\ \Rightarrow PS=4.5\cdot\sin (62.58)=3.99 \\ \cos (62.58)=\frac{\text{adjacent side}}{hypotenuse}=\frac{QS}{4.5} \\ \Rightarrow QS=4.5\cdot\cos (62.58)=2.07 \end{gathered}[/tex]therefore, PS = 3.99 and QS = 2.07
Now, notice that the base of the triangle PQR is:
[tex]QR=QS+SR[/tex]since we already know that SR = 5, we have that the base of the triangle is:
[tex]QR=2.07+5=7.07[/tex]Now we can find the area of the triangle PQR:
[tex]A_{\Delta\text{PQR}}=\frac{\text{base}\cdot\text{height}}{2}=\frac{QR\cdot PS}{2}=\frac{7.07\cdot3.99}{2}=\frac{28.21}{2}=14.11[/tex]therefore, the area of triangle PQR is 14.11 u^2
. MODELING REAL LIFE You save $20 each week to
buy a smart watch that costs $229.95.
a. Describe the numbers of months you need to
save to buy the smart watch.
b. Your parents give you $50 to help you buy
the smart watch. How does this affect your
answer in part (a)? Use an inequality to justify
your answer.
After doing mathematical operations, we can conclude that it would take is 12 months to buy the smart-watch for $229.95 if we save $20 per month.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).help meeeeeeeeeeeeeeeeeeeeeee
thank you
The values of the functions at x = 0 and x = 25/16 are f(0) = 0 and f(25/16) = 5/4
How to evaluate the function?The equation of the function is given as
f(x) = √x
The x values are given as
x = 0, 25/16
This means that
x = 0 and x = 25/16
Substitute x = 0 and x = 25/16 in the equation of the function
So, we have
When x = 0
f(0) = √0
Evaluate
f(0) = 0
When x = 25/16
f(25/16) = √25/16
Evaluate
f(25/16) = 5/4
Hence, the values are 0 and 5/4
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Find the distance between the two points below. If your answer is not aninteger then type it as a decimal rounded to the nearest hundredth.(-4,1) and (3,-4)The distance between the two points is
The distance between two points is defined as follows:
[tex]d(a,b)=\sqrt[]{(x_2-x_1)^2-(y_2-y_1)^2}[/tex]Replacing the points in the equation:
[tex]\begin{gathered} a\to(-4,1) \\ b\to(3,-4) \\ d(a,b)=\sqrt[]{(3_{}-(-4))^2-(-4_{}-1_{})^2} \\ d(a,b)=\sqrt[]{(7)^2-(-5_{})^2} \\ d(a,b)=\sqrt[]{49-25} \\ d(a,b)=\sqrt[]{24} \\ d(a,b)=4.8989 \end{gathered}[/tex]The distance between the two points is 4.89 aprox 4.9
Find the surface area of the rectangular prism.4 yd3 yd3 yd
Surface area of rectangular prism,is'
A=2(wl+hl+hw)
h-height
l-length
w-width
A=2(3X3 + 4X3 + 4X3)
A=66 Sq units
Determine whether the data described below are qualitative or quantitative and explain why.
The blood groups of A, B, AB, and O
Choose the correct answer below.
OA. The data are qualitative because they don't measure or count anything.
OB. The data are quantitative because they consist of counts or measurements.
OC. The data are qualitative because they consist of counts or measurements.
OD. The data are quantitative because they don't measure or count anything.
The given data is qualitative in nature because they do not measure or count anything.
According to the question,
We have the following information:
The blood groups are A, B, AB and O.
Now, we have to find whether this data is qualitative or quantitative in nature.
First, we will first find the definitions of qualitative data and quantitative data. Qualitative data means that the data describes the types, names, symbols or the nature of the objects being studies. It is often the nature of observation that is described in these types of data. For example, if one is studying endangered species then the reasons for their decline is qualitative data.
Quantitative data often gives us the numbers or the count of the object.
Now, in this case, we are not given that there are 4 different blood groups. Instead, we are given the types of blood groups.
So, this is qualitative in nature.
Hence, the correct option is A.
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While shopping at his local home improvement store, Chen notices that the directions for an extension ladder state, “This ladder is most stable when usedat a 75° angle with the ground." He wants to buy a ladder that will reach a height of 26 feet to paint a two-story house. How long does his ladder need tobe? Draw a diagram and set up an equation for this situation. Show all work.
hello
to solve this question, we need to draw a diagram to illustrate their positions
to solve this question, we can simply use trigonometric ratio
SOHCAHTOA
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp} \\ \cos \theta=\frac{adj}{hyp} \\ \tan \theta=\frac{opp}{adj} \end{gathered}[/tex]from this, we can use the sine angle to solve this since the parameters of interests are hypothenus, opposite and angle
[tex]\begin{gathered} \theta=75 \\ \text{hpy}=x \\ \text{opp}=26 \end{gathered}[/tex][tex]\begin{gathered} \sin 75=\frac{26}{x} \\ x=\frac{26}{\sin 75} \\ x=26.917\text{feet} \end{gathered}[/tex]from the calculations above, the length of the ladder is 26.91 feet
A dairy farmer wants to mix a 80 % protein supplement and a standard 70 % protein ration to make 1500 pounds of a high-grade 75 % protein ration. How many pounds of each should he use?
80% of protein supplement mixed with 70% of protein ration to make 1500 pounds of high grade 75% protein ration
so, let the number of pounds from 80% = x
And the number of pounds from 70% = y
Total pounds = 1500 pounds
so, x + y = 1500
The total concentration = 75%
so,
0.8 x + 0.7 y = 0.75 * 1500
So, the system of equations will be:
x + y = 1500 (1)
0.8 x + 0.7 y = 1125 (2)
solve the equations to find x and y
So,
Multiply the first equation by -0.7
-0.7 x - 0.7 y = -0.7 * 1500
-0.7 x - 0.7 y = -1050 (3)
Add the equations (2) and (3)
(0.8 x + 0.7y) + ( -0.7x - 0.7y ) = -1050 + 1125
0.8 x - 0.7 x + 0.7 y - 0.7 y = 75
0.1 x = 75
divide both sides by 0.1
x = 75/0.1 = 750
Substitute with x at the equation (1)
750 + y = 1500
y = 1500 - 750 = 750
so, the number of pounds from 70% = 750 pounds
And the number of poinds from
8. Multi-Step Willie bagged his potatoes
in 18 ten-pound bags, 16 five-pound bags,
and 4 twenty-five pound bags. He has
2 pounds of potatoes left over. How many
pounds of potatoes does Willie have?
The total pounds of the potatoes Willie have is 362 pounds.
What is defined as the term addition?Addition is a method of combining items and counting them as a single large group. In mathematics, addition is the method of integrating two or more numbers together. The numbers added are referred to as addends, and the result or final answer obtained after the method is referred to as the sum.For the given question.
Multi-Step Willie bagged his potatoes in -
18 ten-pound bags, 16 five-pound bags,4 twenty-five pound bags,2 extra pounds of potatoes.Thus, the total pounds of the potatoes are-
Total potatoes = 18×10 + 16×5 + 4×25 + 2
Total potatoes = 362
Thus, the total pounds of the potatoes Willie have is 362 pounds.
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The satang coin from Thailand has a radius of about 7 mm The diameter is mm The circumference in terms of his v mm 22 Using 7 for at the approximate value of the circumference is v mm Intro Donation. what is it
Write an equation of the line with the given slope and containing the given point. Write the equation in the form y = mx + b.
Slope -4; through (-3, -6)
Group of answer choices
y = -4x - 18
y = -4x + 18
y + 6 = x + 3
Answer:
y = -4x - 18
Step-by-step explanation:
Slope: -4; (-3, -6)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-6) = -4 (x - (-3)
y + 6 = -4 (x + 3)
y + 6 = -4x - 12
-6 -6
------------------------
y = -4x - 18
I hope this helps!
Its just the circled ones, numbers 1,3,4,and 6. I've been unable to understand anything recently so help is greatly appreciated
Given:
The expression is,
[tex](-6x^2+3x-7)+(10x^2+4x-2)[/tex]Explanation:
Evaluate the sum of two expression.
[tex]\begin{gathered} (-6x^2+3x-7)+(10x^2+4x-2)=-6x^2+10x^2+3x+4x-7-2 \\ =4x^2+7x-9 \end{gathered}[/tex]So answer is,
[tex]4x^2+7x-9[/tex]A sweater is on sale at the mall for 75% off the original price of $38.00. What is the new price of the sweater?
We have:
Original price = $38.00
Off = 75% = 0.75
Then:
[tex]0.75\times38.00=28.5[/tex]So, the new price of the sweater is:
[tex]38.00-28.5=9.5[/tex]Answer: $9.5
Write the point slope form of the equation of a line passing through (-1,4) and (-4,2)
The equation of a line in the point slope form is expressed as
y - y1 = m(x - x1)
Where
m represents slope
y1 represents intial value of y
x1 represents initial value of x
The formula for determining slope is expressed as
m = (y2 - y1)/(x2 - x1)
y2 and x2 are final values of y and x respectively.
From the information given,
x1 = - 1, x2 = - 4
y1 = 4, y2 = 2
Slope = (2 - 4)/(- 4 - - 1)
Slope = - 2/ (- 4 + 1)
Slope = - 2/- 3
m = 2/3
Substituting m = 2/3, y1 = 4 and x1 = - 1 into the point slope equation, it becomes
y - 4 = 2/3(x - - 1)
= y - 4 = 2/3(x + 1)
6 more than the quotient of a number and five is eight use the variable B for the unknown number
Let B the unknown number.
The quotient of this number and five can be express as:
[tex]\frac{B}{5}[/tex]Six more than the quotient of a number and five can be express as:
[tex]\frac{B}{5}+6[/tex]Finally we know that this is equal to eight, then we have the equation:
[tex]\frac{B}{5}+6=8[/tex]Solving for B we have that:
[tex]\begin{gathered} \frac{B}{5}+6=8 \\ \frac{B}{5}=8-6 \\ \frac{B}{5}=2 \\ B=5\cdot2 \\ B=10 \end{gathered}[/tex]Therefore the unknown number is 10
what is the answer to 13 /5/6 - 17 /3/8
When the fractions, 13 5/6 and 17 3/8 are subtracted, the answer would be -3 ⁵ / ₁₂
How to subtract mixed fractions?To subtract mixed fractions, the first thing to do is to convert the mixed fraction to an improper fraction.
To convert improper fractions, multiply the denominator by the whole number and then add the numerator. The result would be the numerator.
Converting the fractions gives:
13 5/6 = 83 / 6
17 3/8 = 139 / 8
Subtracting these fractions then gives:
= 83 / 6 - 139 / 8
Find a common denominator for 6 and 8 which will be 24 as this is their lowest common multiple.
Then, divide 24 by the denominator and multiply the result by the numerator of the fraction:
= 332 / 24 - 417 / 24
= -85 / 24
= - 3¹⁰ /₂₄
= -3 ⁵ / ₁₂
In conclusion, the answer would be -3 ⁵ / ₁₂
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please help this is for my study guide thanks! (btw it says simplify)
To simplify:
[tex](2b^2a)(4ba^2)[/tex]On simplification, we get
[tex]\begin{gathered} (2b^2a)(4ba^2)=8b^{2+1}a^{1+2} \\ =8b^3a^3 \end{gathered}[/tex]Hence, the answer is,
[tex]8b^3a^3[/tex]Suppose f(x) represents the amount of money in a bank account after x weeks.If you want to represent the amount of money in a bank after 7 weeks, what should you write instead of f(x)?
Since f(x) represents the amount of money in a bank account after x weeks and we want to know the money after 7 weeks we need to plug x=7 in the function, that is we need to write f(7).
According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=-4x^6 - 3x^5+2x² - 4x +1? Drag the choices to the boxes to correctly complete the table.
[tex] -4x^6 - 3x^5+2x^2 - 4x +1 = 0[/tex] has 1 or 3 Positive roots and one only Negative roots.
Descartes' rule of sign.Function has the same number of positive real zeroes as there are number of changes in the sign of the coefficients, or an even number less than the found number.
Now, here the given expression is : p(x) = [tex] -4x^6 - 3x^5+2x^2 - 4x +1 [/tex]
Now here, the number of sign changes are:
First : + to - in [tex] - 3x^5 => + 2x^2 [/tex]
Second : - to + in [tex]+2x² => - 4x [/tex]
Third: + to - in [tex] - 4x => +1 [/tex]
So, the total sign changes = 3
⇒ The total positive roots of p(x) = 3 or a EVEN NUMBER LESS THAN 3 = 1.
So, p(x) has either 3 or 1 POSITIVE ROOTS.
⇒ The number of negative roots p(x) has is either 4 or 6.
Hence has 1 or 3 Positive roots.
Now I look at f (−x). That is, having changed the sign on x, I'm now doing the negative-root case:
p(-x) = [tex] -4(-x)^6 - 3(-x)^5+2(-x)^2 - 4(-x) +1 [/tex]
= [tex] -4x^6 + 3x^5+2x^2 + 4x + 1 [/tex]
the number of sign changes are:
First : + to - in [tex] -4x^6 => +3x^5 [/tex]
So, the total sign changes = 1.
so there is exactly one negative root. (In this case, I don't try to count down by two's, because the first subtraction would give me a negative number.)
Hence has 1 or 3 Positive roots and one only Negative roots.
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d 2 6.28 3 9.42 5 15.7 What is the constant of proportionality? Type your answer below as a number texample: 5.3.1. + H2. or 3/2):
Ok,we can calculate the constant of proportionality as the slope of a line
with this equation
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a point to the right compared to (x1, y1)
for this case I will choose the points (2,6.28) and (3,9.42)
where (3,9.42) is (x2,y2)
[tex]\begin{gathered} m=\frac{9.42-6.28}{3-2} \\ m=\frac{3.14}{1} \\ m=3.14 \end{gathered}[/tex]if we want a more exact number we can divide one number by another
[tex]\begin{gathered} \frac{6.28}{2}=3.14 \\ \frac{9.42}{3}=3.14 \\ \\ \frac{15.7}{5}=3.14 \end{gathered}[/tex]so the correct constant of proportionality is 3.14
If it takes Carlos 15 weeks to make 3 birdhouses, how long will it take him to make 11 birdhouses?
Applying proportion
we have that
15 weeks/ 3 birdhouses=x/11 birdhouses
solve for x
x=(15/3)*11
x=5*11
x=55 weeks