Given:
The volume of the cubic prism is 45 cubic inches.
Let the side length = x
So,
[tex]volume=x^3=45[/tex]Taking the cubic root of 45
[tex]x=^3\sqrt[]{45}\approx3.557[/tex]So, the answer will be the side length = 3.557 inches
Which equivalent equation is the result of applying the distributive property in thegiven equation?10y + 14 = 2(y-9)
Answer
[tex]10y+14=2y-18[/tex]Explanation
The distributive property tells us that:
[tex]a(x+y)=ax+ay[/tex]Thus, we can apply this property to our given equation in the right side:
[tex]10y+14=2(y-9)[/tex][tex]10y+14=(2\cdot y-2\cdot9)[/tex][tex]10y+14=2y-18[/tex]find linear approxmiation f(x)=x^3+5x^2+4 at a=1
The linear approximation of the function is given by a³ - 3a² +4 + 10ax
The given function is f(x)=x³+5x²+4
Let us find the linear approximation.
L(a) = f(a) + f'(a)(x-a)
let us differentiate the function
f'(x) = 2x²+10x
Let us find the value of the function at the exact point a
f'(a) = 2a²+10a
f(a) = a³+5a²+4
L(a) = f(a) + f'(a)(x-a)
L(a) = a³ + 5a² + 4 + 2a² + 10a (x-a)
L(a) = a³ + 7a² +4 + 10ax - 10a²
L(a) = a³ - 3a² +4 + 10ax
The use of a line to approximate the value of a function at a point is the definition of a linear approximation of either a function. When we see a curve (of a function) and a point on it, we immediately think of the tangent line concept.
If the equation of the tangent line is discovered at the supplied point, one can roughly calculate the value of something similar to the function at every location that is very close to the supplied point using the equation of the tangent line. This concept is also known as the tangent line approximation because the tangent line is utilized. Additionally called linear approximation.
Therefore the linear approximation of the function is given by
a³ - 3a² +4 + 10ax .
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The mean mark for the class was 70% there are 30 students in class 20 of whom are boys the mean mark for the mark in test was 62% work out mean for the girls.
The mean mark of the girls is 86.
How is the mean mark calculated?You must first add up all the numbers (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47) before you can determine the mean. The amount is then divided by the number of scores utilized (47 / 7 = 6.7).
Given information:
The number of total students in the class is 30
Given number of boys in the class is 20
Then, the number of girls will be = 30-20
=10
The mean mark of the class = 70×30
= 2100
The guy's average grade is = 62.
Then, mark for the boys = 62×20
= 1240
The mark for the girls = 2100-1240
= 860
Then the mean mark of the girls will be =860/10
= 86
Hence, the mean mark for the girls is 86
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use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.
We are given the following expression:
[tex]\log a-3\log b+4\log c[/tex]we are asked to simplify this expression. To do that we will first use the following property:
[tex]a\log b=\log ^{}b^a[/tex]we will apply this to the second and third terms, like this:
[tex]\log a-\log b^3+\log c^4[/tex]Now we will use the following property:
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]we will use this property for the first and second terms:
[tex]\log (\frac{a}{b^3})+\log c^4[/tex]Now we will use the following property:
[tex]\log a+\log b=\log ab[/tex]We will use the property in the last two terms, like this:
[tex]\log (\frac{ac^4}{b^3})[/tex]And thus, we have simplified the logarithmic expression into one single logarithm
Xavier Knox's annual salary is $61,100. He is paid semimonthly. His personal exemptions total $4,000. How
much does his employer deduct from each of Knox's paychecks for state income tax of 3.5 percent?
a. $166.54
c.
b. $83.27
$83.13
d. $166.26
The amount that Xavier Knox's employer deducts from his paychecks for state income tax is b. $83.27
How to find the state income tax?First find his taxable income:
= Annual salary - Personal exemptions
= 61, 100 - 4, 000
= $57, 100
The state income tax per year is:
= 57, 100 x 3.5% state income tax rate
= $1, 998.50
The semimonthly state income tax deducted is:
= 1, 998.50 / (12 months x twice a month)
= $83.27
In conclusion, on a semimonthly basis, $83.27 is deducted for state income tax.
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Yvette maps out several locations in her town, with distances and angles between them. Two triangles are formed within the map.
To conclude that these triangles are congruent by SAS Congruence Postulate, what must the distance between the school and the park be
To be both triangles to be congruent the distance between the school and the park be 1.1 miles.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
As per the given two triangles,
The side 2.7 miles is the common side.
The angle is 52 degrees in both triangles same.
To be congruent any one side must be the same by the SAS rule.
Thus, the school-to-park corresponding side is school-to-store.
school to park = 1.1 miles
Hence "To be both triangles to be congruent the distance between the school and the park be 1.1 miles".
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An irregular figure is shown on the coordinate plane below. Part A: Find the area of the irregular figure above. Answer:__________________________ square units
In the present question, we will calculate the area of each of the three regular figures that are parts of the irregular figure. They are:
A: a rectangle 4x3
B: a rectangle 9x3
C: a rectangle 3x5
The area of each rectangle is just the multiplication of the two sides, and the area of the irregular figure is the sum of them. From this, we calculate:
[tex]\begin{gathered} A_A=4\times3=12\text{ square units} \\ A_B=9\times3=27\text{ square units} \\ A_C=3\times5=15\text{ square units} \\ \\ A_{\text{Total}}=A_A+A_B+A_C \\ A_{\text{Total}}=12+27+15=54\text{ square units} \end{gathered}[/tex]From the solution presented above, we are able to conclude that the area of the irregular figure is 54 square units.please help me dhdjjdjejejejdjejejejejejkenensndd
Answer: area=8cm
Step-by-step explanation:
Answer:
a) Area of shape = 8 square cm.
Step-by-step explanation:
Area of composite shape:
Area of shape = area of rectangle + 2* area of triangle
Rectangle:l = 3 cm ; w = 2 cm
[tex]\sf \boxed{\text{Area of rectangle = l *w}}[/tex]
= 3 * 2
= 6 cm²
Triangle:
b = 2 cm
h = 1 cm
[tex]\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}[/tex]
[tex]\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2[/tex]
Area of two triangles = 2 *1
= 2 cm²
Area of shape = 6 + 2
= 8 cm²
b) Area of rectangle ABCD = 4 * 2
= 8 cm²
there are 55 stickers in each box how many stickers are in 7 boxes
Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
SOLUTION
The coordinate of the vector P and Q are
[tex]\begin{gathered} P(-13,\text{ 11)} \\ \text{And } \\ Q(-18,2) \end{gathered}[/tex]To find the vector PQ. we have
[tex]\begin{gathered} t=\bar{PQ} \\ PQ\text{ is having the coordinate } \\ PQ=(-18-(-13),2-11)=(-5,-9) \end{gathered}[/tex]To find the vector, we use
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \text{Where } \\ x=-5,y=-9 \\ r=\sqrt[]{(-5)^2+(-9)^2}=\sqrt[]{25+81}=\sqrt[]{106}=10.296 \end{gathered}[/tex]Then we obtain the angle using
[tex]\begin{gathered} \text{tan}\theta=(\frac{y}{x})_{} \\ \text{Substituting the value of x and y, we have } \\ \tan \theta=(\frac{9}{5})=\tan \theta=(1.8) \end{gathered}[/tex]Hence
[tex]\begin{gathered} \tan \theta=1.8 \\ \theta=\tan ^{-1}(1.8) \\ \theta=60.945 \end{gathered}[/tex]Hence
The vector in trigonometry form will be
[tex]\begin{gathered} t=r(i\cos \theta+j\sin \theta) \\ \text{Then} \\ t=10.296\cos 60.945i+10.296\sin 60.945j \end{gathered}[/tex]Therefore
t= 10.296 cos 60.945 i + 10.296 sin 60.945j
Answer: Option C(third option ).
I need help please with [tex]6409 \div 61[/tex]. I know the answer is 105.06the problem is it has to be written as a a whole number with a fraction. we put 105 and 3/50 but its saying it's wrong.
Given the expression
[tex]\frac{6409}{61}[/tex]Next is to know how many 61 can go in 6409. Using the calculator, you can see that it is 105 with a remainder of 4
We will then have to express the fraction in the form:
[tex]Q\text{ +}\frac{R}{D}[/tex]Q is the quotient = 105
R is the remainder = 4
D is the divisor = 61
Substituting these values into the expression we will have:
[tex]\begin{gathered} \frac{6409}{61}=105+\frac{4}{61} \\ \frac{6409}{61}=105\frac{4}{61} \end{gathered}[/tex]Hence the solution written as a whole number and fraction is 105 4/61
A bag contains 15 cards numbered 1 through 15. A card is randomly chosen from the bag. What is the probability that the card has an odd number on it? Write your answer as a fraction in simplest form.
There are 15 cards numbers are from 1 to 15.
From the numbers 1 to 15:
• 8 numbers, are ,odd
,• 7 numbers, are ,even,
The probability is the possibility of an event occuring.
Probability of event to happen P(A) = Number of favourable outcomes/Total Number of outcomes
Thus, the probability of an odd card is:
total number of odd cards/total number of cards
= 8/15
the Correct Answer is:
[tex]\frac{8}{15}[/tex]what is the 1/3 of 24
ANSWER:
8
STEP-BY-STEP EXPLANATION:
They ask us for 1/3 of 24, what we must do multiply both values, just like that
[tex]\frac{1}{3}\cdot24=8[/tex]Which means that 1/3 of 24 is 8
There are f flavors of ice cream at the shop. Dominic has sampled 7 of them. Choose the expression that shows the number of flavors Dominic has not sampled.
In linear equation, Jen planned to spent 3.75 hours paddleboarding.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Dominic has sampled = 7
flavors of ice cream at shop = f
the expression that shows the number of flavors Dominic has not sampled
= 7 * f = 7f
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Lines AB, CD, and LK intersect as shown in the figure below. AB I CDKA
The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent.
Given that:
[tex]\begin{gathered} m\angle\text{LRB}=86\degree,\text{ its alternate exterior angle is }m\angle\text{CSK} \\ \\ \text{Therefore,} \\ m\angle\text{CSK}=m\angle\text{LRB} \\ m\angle\text{CSK}=86\degree\text{ (final answer)} \end{gathered}[/tex]If the simple interest on $6,000 for 5 years is $2,400 then what is the interest rate?
The interest rate will be 8%.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Principal amount = $6,000
Time = 5 years
Simple interest = $2,400
Now,
We know that;
⇒ Simple interest = PRT
Where, P is principal amount, R is interest rate and T is time.
Substitute all the values, we get;
⇒ Simple interest = PRT/100
⇒ 2400 = 6,000 x R x 5/100
⇒ 2400/30,000 = R/100
⇒ R = 0.08 x 100
⇒ R = 8%
Thus, The interest rate will be 8%.
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I don't understand this
Answer:
∠F = 29
Step-by-step explanation:
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
58 = x + x
58 = 2x
2x = 58
x = 58/2
x = 29
∠F = x = 29
-1.25(z+8)=-6
Please help; find z
Answer:
z = -3.2
Step-by-step explanation:
-1.25(z + 8) = -6
-1.25z - 10 = -6
+10 +10
-----------------------
-1.25z = 4
÷(-1.25) ÷(-1.25)
--------------------------
z = -3.2
I hope this helps!
16 oz harbor peanut butter for 2.49 or a 64 oz jar of peanut butter for 6.99 round everything up to the nearest cent or hundreth. yes mam
We have to find the "better buy" between two options:
1) 16 oz jar for $2.49
2) 64 oz jar for $6.99
We can compare this two options with the unit price of each one. The unit price will be expressed in "$ per oz" or "$/oz". The option with the smaller unit price is the "better buy".
We can calculate the unit price as teh quotient between the price and the weight of each option.
Unit price for Option 1:
[tex]u_1=\frac{2.49\text{ \$}}{16\text{ oz}}\approx0.16\frac{\$}{oz}_{}[/tex]Unit price for Option 2:
[tex]u_2=\frac{6.99\text{ \$}}{64\text{ oz}}\approx0.11\frac{\$}{oz}[/tex]As the Option 2 (64 oz jar) has a smaller unit price, the better buy is the 64 oz jar for $6.99.
Answer: the better buy is the 64 oz jar for $6.99.
Find the distance between the points J(-8, 0) and K(1, 4).
The distance between two points of coordinates (x₁, y₁ ) and (x₂, y₂) is calculated using the formula:
[tex]undefined[/tex]What is the common difference for the arithmetic sequence?
3.2, 5, 6.8, 8.6, 10.4
help me please!
Answer:
the difference is 1.8
Step-by-step explanation:
5-3.2=1.8
6.8-5=1.8
8.6-6.8=1.8
ect
2. The following data set is given:5041414546364436513736494345454136Construct a dot plot:
As given by the question
There are given that the numbers;
[tex]50,\text{ 41, 41, 45, 46, 36, 44, 36, 51, 37, 36, 49, 43, 45, 45, 41, 36.}[/tex]Now,
First make a table of numbers and their frequency.
So,
[tex]\begin{gathered} \text{Number}\rightarrow\text{frequency} \\ \text{ }36\rightarrow4 \\ \text{ 37}\rightarrow1 \\ \text{ }44\rightarrow1 \\ \text{ 45}\rightarrow3 \\ \text{ 46}\rightarrow1 \\ \text{ 49}\rightarrow1 \\ \text{ 50}\rightarrow1 \\ \text{ 51}\rightarrow1 \\ \text{ 41}\rightarrow3 \\ \text{ 43}\rightarrow1 \end{gathered}[/tex]Now,
From the dot plot of the given numbers and their frequency.
So,
The dot plot of the given number is shown below:
I don’t under stand help
5.5/x=1.375/11
find x
Answer:x=44
Step-by-step explanation:
Rides, r Cost, c5 $25.506Use the table shown to answer problems10-11.10. A state fair charges $8 for generaladmission and $3.50 for each ride. Usethe pattern in the table to find the cost of7 rides and 10 rides. Then write anequation for the pattern.11. Find the cost c for 18 rides.$29.0078$36.0010C= 8 + 3.50rUse the operation symbols in the math palette as needed. Type an equation. Use integers or decimals for anynumbers in the equation.)11. Find the cost c for 18 rides.
We want to know the cost for 7 rides and for 10 rides. We see that for each ride the price increases by $3.50. And thus the price for 7 rides will be:
[tex]29.00+3.50=32.50[/tex]And the price for 10 rides will be:
[tex]36.00+3.50+3.50=39.50+3.50=43.00[/tex]Now, for finding the equation we use that the state fair charges $8 for a general admission, and $3.50 for each ride. This can be written as:
[tex]y=8+3.50x[/tex]where x represents the number of rides.
For example, if we want to know the cost for 18 rides, we replace the value of x by 18, and we get:
[tex]\begin{gathered} y=8+3.50(18) \\ =8+63 \\ =71 \end{gathered}[/tex]Then, the cost for 18 rides is $71.
Round 31.212 to the nearest hundredth.
☐
Answer:
31.21
Step-by-step explanation:
Given: A = B,
CD LAB
Prove: CD bisects ACB
C
A
D
B
As AD = DB, CD bisects ∠ACD
In Δ ACD and ΔBCD
We need to prove that CD bisects ACB
∠A = ∠B
side AC = CB (as angle A and angle B are same)
CD is ⊥ AB
So, ∠ADC = ∠BDC
By SAS Δ ACD and ΔBCD are congurent
In congurent triangles, corresponding angles and sides are equal
So, in Δ ACD and ΔBCD
ACD = DCB
Therefore, as AD = DB, CD bisects ∠ACD
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A yearbook has 32 pages, and each page has 8 pictures on it. Estimate how manypictures are in the yearbook.
To find how many picture are in the yearbook, multiply the number of pages of the yearbook by the number of pictures on one page. This is 32 times 8:
[tex]32\cdot8=256[/tex]There are 256 picture in the yearbook.
Estimate the sum or difference, by rounding each number to its largest place (front-end rounding)–36.673+39.999
Answer:
0
Explanation:
Given the difference:
[tex]-36.673+39.999[/tex]In front-end rounding, we consider the number with the largest place value.
In -36.673, the number with the largest place value is 3.
The digit after 3 us 6, so we round up as follows:
[tex]-36.673\approx-40[/tex]Likewise, In 39.999, the number with the largest place value is 3.
The digit after 3 us 9, so we round up as follows:
[tex]39.999\approx40[/tex]Therefore:
[tex]-36.673+39.999\approx-40+40=0[/tex]The diffrence is 0 using front-end rounding.
Make a table of the values for the function Y=3/5x-1
Answer:
plug the the x values in the chart into the formula one at a time and plug it into a calculator to get your y values.
example: y= -3/5(10)-3 —-> -9 y value
Step-by-step explanation: