Answer:
x=60
Step-by-step explanation:
right angle is 90 degrees +30 degrees equals 120 so 180-120 gives you 60 degrees
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Answer:
I think it's A. 32.0
Step-by-step explanation:
Gabe deposits $2,500 into each of two savings accounts.
Account ONE earns 4% annual simple interest.
Account TWO earns 4.5% interest compounded annually.
What is the sum of the balances of Accounts ONE and TWO at the end of 3 years?
Answer:
637.5 I think it's right
Step-by-step explanation:
2,500x.04=100x3=300
2,500x.045=112.5x3=337.5
300+337.5=637.5 interest
2,500x2+637.5=5,637.5
Answer:
$5,612.16
Step-by-step explanation:
Part 1) Account I earns 4% annual simple interest.
we know that
The simple interest formula is equal to A = P (1+rt)
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have:
t = 3 years
P = $2,500
r = 4% = 4/100 = 0.04
substitute in the formula above
A = 2,500 (1 + 0.04 * 3)
A = 2,500 (1.12)
A = $2,800
Part 2) Account II earns 4% interest compounded annually.
we know that
The compound interest formula is equal to: A = P (1 + r/n)nt
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
t = 3 years
P = $2,500
r = 4% = 4/100 = 0.04
n = 1
substitute in the formula above
A = 2,500 * (1 + 0.04/1)3
A = 2,500 * (1.04)3
A = $2,812.16
Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?
Sum the two final investment:
$2,800 + $2,812.16 = $5,612.16
Factor the polynomial completely. Use synthetic division.
F(x) = x^3-7x-6
Answer:
The factors of given polynomial x =-1 , -2 and x =3
Step-by-step explanation:
Step(i):-
Given the polynomial
f(x) = x³ - 7x -6
put x =-1
f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0
(x+1) is a one factor
By using synthetic division
x³ x² x constant
x=-1 ↓ 1 0 -7 -6
↓ 0 -1 1 6
1 -1 -6 0
The polynomial x² - x - 6
Step(ii):-
The factors ( x+1)(x² - x - 6 ) = 0
x = -1 and x² - x - 6 =0
x =-1 and x² - 3x + 2 x - 6 =0
x =-1 and x (x -3) + 2( x-3) =0
x =-1 and (x+2)(x-3) =0
Final answer:-
The factors of given polynomial x =-1 , -2 and x =3
what assumption have you made in answering part b
You're assuming that this data set represents all of Mrs. Hassaan's pupils. Certain students could be missing from the histogram - for instance, there could be one or two students who missed the test, but for certain reasons will be taking a make-up exam. Their grade would not be recording in this data set, but they still contribute to the class size, and so would be unaccounted for here.
Tom bought a pen for $30
and sold it to gain
20% on his cost price. How much money
did he gain?
Answer:
he gained 6 dollars
Step-by-step explanation:
30 x 0.2
Tom bought a pen for $30 and sold it to gain 20% on his cost price that he gained 6 dollars.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Lets suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
It is given that Tom bought a pen for $30 and sold it to gain 20% on his cost price.
Therefore,
30 x 20%
30 x 0.2 = 6 dollars
Thus, he gained 6 dollars.
Hence, Tom bought a pen for $30 and sold it to gain 20% on his cost price that he gained 6 dollars.
Learn more about unit price here:
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Can someone tell me how to do a transversal angle measurement with steps and angles
Answer:
Sorry I am not sure but when I figure it out..... I prolly won't
Step-by-step explanation:
Answer:
When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles . If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary
Step-by-step explanation:
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What are the .95 (5 percent risk of Type I error) upper and lower control limits for the p-chart
Answer:
Prof B and Prof D
Step-by-step explanation:
Step-by-step explanation:
From the question we are told that
Sample size 100
Instructor Number of Failures
Prof. A 13
Prof. B 0
Prof. C 11
Prof. D 16
Confidence level= 0.95
From Z table
Z=1.96
Generally proportion for failure is mathematically given as
[tex]Proportion\ of\ Failure\ P=\frac{Number\ of\ Failure\ N}{Sample\ size\ S}[/tex]
[tex]P=\frac{N}{S}[/tex]
For Prof A
[tex]P_A=\frac{N_A}{S}[/tex]
[tex]P_A=\frac{13}{100}[/tex]
[tex]P_A=0.13[/tex]
For Prof B
[tex]P_B=\frac{N_B}{S}[/tex]
[tex]P_B=\frac{0}{100}[/tex]
[tex]P_B=0[/tex]
For Prof C
[tex]P_C=\frac{N_C}{S}[/tex]
[tex]P_C=\frac{11}{100}[/tex]
[tex]P_C=0.11[/tex]
For Prof D
[tex]P_D=\frac{N_D}{S}[/tex]
[tex]P_D=\frac{16}{100}[/tex]
[tex]P_D=0.16[/tex]
Generally the average proportional failure is mathematically given as
[tex]P_a_v_g=\frac{0.13+0+0.11+0.16}{4}[/tex]
[tex]P_a_v_g=0.10[/tex]
Therefore having this we calculate for the control limits
Generally the upper control limit UCl is mathematically given as
Upper control limits:
[tex]UCL =P_a_v_g +Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }[/tex]
[tex]UCL =0.1 +1.96\sqrt{\frac{0.1(1-0.1) }{100}}[/tex]
[tex]UCL =0.1 +1.96*0.03[/tex]
[tex]UCL =0.1 +0.0588[/tex]
[tex]UCL =0.1588[/tex]
Generally the upper control limit UCl is mathematically given as
Lower limit control limits:
[tex]UCL =P_a_v_g _Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }[/tex]
[tex]UCL =0.1 -1.96\sqrt{\frac{0.1(1-0.1) }{100}}[/tex]
[tex]UCL =0.1 -1.96*0.03[/tex]
[tex]UCL =0.1 -0.0588[/tex]
[tex]UCL =0.0412[/tex]
Therefore the Range is 0.0412 to 0.1588
Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options
What is the correct sequence of steps for calculating 9^6 on the scientific calculator?
First press 9, then 6, then the exponent key, and finally press the equal sign (-).
First press 6, then9, then the exponent key, and finally press the equal sign ().
First press 9, then the exponent key, then 6, and finally press the equal sign (-).
Answer:
C
Step-by-step explanation:
First press 9, then the exponent key, then 6, and finally press the equal sign.
The perimeter of a rectangle is 120 centimeters. The base is 3 times the height. What are the dimensions of the rectangle? a. h = 9cm, b = 18 cm c. h = 15 cm, b = 45 cm b. h = 19 cm, b = 57 cm d. h = 10 cm, b = 15 cm
Answer:
[tex]Height = 15[/tex]
[tex]Base = 45[/tex]
Step-by-step explanation:
Given
Shape: Rectangle
[tex]Perimeter = 120cm[/tex]
[tex]Base = 3 * Height[/tex]
Required
Determine the dimensions
The perimeter of a rectangle is:
[tex]Perimeter = 2 * (Base + Height)[/tex]
Substitute 120 for Perimeter
[tex]120 = 2 * (Base + Height)[/tex]
Divide both sides by 2
[tex]60 = Base + Height[/tex]
Substitute 3 * Height for Base
[tex]60 = 3 * Height + Height[/tex]
[tex]60 = 3Height + Height[/tex]
[tex]60 = 4Height[/tex]
Divide both sides by 4
[tex]15 = Height[/tex]
[tex]Height = 15[/tex]
Substitute 15 for Height in [tex]Base = 3 * Height[/tex]
[tex]Base = 3 * 15[/tex]
[tex]Base = 45[/tex]
2(5x+7)=16
what the answer?
Answer:
x = 1/5
Step-by-step explanation:
2(5x + 7) = 16
2 * 5x + 2 * 7 = 16
10x + 14 = 16
10x = 16 - 14
10x = 2
x = 2/10
x = 1/5
In the diagram the radius of the outer circle is 2x cm and the radius of the inner circle is 6 cm. The area of the shaded region is 160
let's find the area of the outer circle and the inside circle
the inside's circle area
A= π x 6²=36π
the outer's
A' = π x 4x²= 4πx²
A'-A=4πx²- 36π=160πcm² equivalent to x²- 9=40, so x²=49 implies x =sqrt(49)=7, x=7.
HELP!!! Pleaseeeeeeeeeeeeee
9514 1404 393
Answer:
(b) g(x) = -f(x+3)
Step-by-step explanation:
The dashed-line graph is a reflection over the x-axis and a left-shift by 3 of the solid-line graph. To reflect the function over the x-axis, negate it.
f(x) ⇒ -f(x) . . . . reflected over the x-axis
To translate a function to the right horizontally by "h" units, replace x in the function with (x-h). Here, we want a left shift, so h=-3. That is, x is replaced by (x+3).
Both transformations together give you ...
g(x) = -f(x+3)
Very Short Answer Questions
3. The total surface area of a cube is 1,944 sq cm. Find its side.
35 points and will be mark as brainlist
[tex]\huge\bf\underline{Answer}[/tex]
Given :- Total surface area of a cube = 1944cm²To Find :- Side of the cubeFormula :-[tex]\boxed{\huge \sf{TSA = 6a²}}[/tex]
Where, TSA = Total surface area of a cubea = Side of a cubeSolution :-Let the Side of a cube be 'x'
By substituting values according to the formula,[tex]\sf{:⇒6(x) ^{2} } = 1944cm^{2} [/tex]
[tex]\sf{:⇒ {x}^{2} = \dfrac{1944}{6} }[/tex]
[tex]\sf{:⇒ {x}^{2} = 324}[/tex]
[tex]\sf{:⇒x = \sqrt{324} }[/tex]
[tex]\sf{:⇒x = 18cm}[/tex]
Hence, The Side of a cube is 18cmAt Mary’s fruit stand, a basket of cherries costs $4 and a basket of peaches costs $9. In one morning, Katya sells 96 baskets for $644. How many baskets of peaches were sold?
Answer:
The number of strawberry baskets sold was 44
Step-by-step explanation:
Let
x ----> the number of strawberry baskets sold
y ---> the number of raspberries baskets sold
we know that
In one morning, Katya sells 96 baskets for $644
so
----> equation A
---> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (44.52)
see the attached figure
therefore
The number of strawberry baskets sold was 44 and the number of raspberries baskets sold was 52
Determine the slope and the Y-intercept of each linear equation. y = 6x
Answer:
Slope = 6
Y intercept = 0
Step-by-step explanation:
Given equation is: y = 6x
Equating it with y = mx + b
We find:
Slope m = 6
Y intercept b = 0
the area of a rectangle is 49.7cm2, and the width the rectangle is 3.5 cm what is the length rectangle cenimeters
Answer:
Answer = 14. 2
Step-by-step explanation:
Area of rectangle = length x breath
So, area here is = 49.7 cm2
Breath = 3.5 cm
49.7 = length x 3.5
Length = 49.7 ÷ 3.5
Length = 14.2 cm
I GIVEEE BRAILILSTTTTTTTT
Answer:
umumumuykik.iu.fg
Step-by-step explanation:
lui;iou;uyfluylfuy;lui;uy;
I GIVEEE BRAINLI8LSTT C
Answer:
3,-2.
Step-by-step explanation:
hope this helps. :-)
You are filling a 2-liter bottle with liquid from full 80-milliliter containers. How many containers will it take to fill the 2-liter bottle?
Answer:
25 bottles
Step-by-step explanation:
2 litres=2000 milliliters
2000/80=25 (or) 80x25=2000
The amount of containers it will take to fill the 2-liter bottle is 25 containers.
Given the following data:
Volume of bottle = 2 LitersVolume of containers = 80 milliliterTo determine the amount of containers it will take to fill the 2-liter bottle:
In this exercise, you're required to determine the amount of 80-milliliter containers that would be required to fill the 2-liter bottle.
First of all, we would convert the volume in liters to milliliter.
Conversion:
1 Liter = 1000 millimeters
2 Liter = 2000 millimeters
Now, we can find the amount of containers by using the formula:
[tex]Number\;of\;containers = \frac{Volume \;of\;bottle}{Volume \;of\;containers}[/tex]
Substituting the parameters into the formula, we have;
[tex]Number\;of\;containers = \frac{2000}{80}[/tex]
Number of containers = 25 containers
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what’s 100/12 as a mixed number
Answer: 8 1/3
Step-by-step explanation:
100/12 = 8.33333333
8 4/12
8 1/3
algebra 2!! please help im begging. i don’t understand this at all. thank you!
Answer:
Step-by-step explanation:
so the square root of 6 is the multipyed number of 8 plus 2 divided by9 is to times 8 plus 6
if a number, n, divided by 8 equals 2.5, what is n?
Answer:
n is 20
Step-by-step explanation:
If n/8=2.5, then you can just do 8*2.5 to find n. 2.5*8=20
Answer:
n=20 because if you multiple 2.5 and 8 you will get 20 so if you divide 20 and 8 then you get 2.5
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 10 insects will die
Answer:
The probability that exactly 10 insects will die
P( X = 10 ) = 0.06385
Step-by-step explanation:
Step(i):-
Given a certain insecticide kills 60% of all insects in laboratory experiments
Given proportion p = 0.60
q = 1 - 0.60 = 0.40
Given sample size 'n' = 12
Step(ii):-
Let "X' be the random variable of binomial distribution
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that exactly 10 insects will die
[tex]P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}[/tex]
[tex]n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66[/tex]
[tex]P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385[/tex]
Final answer:-
The probability that exactly 10 insects will die
P( X = 10 ) = 0.06385
what is 4855/200 simplified
Answer:
The answer is 2427.5
Step-by-step explanation:
The fraction consists of two numbers and a fraction bar: 4,855/200
The number above the bar is called numerator: 4,855
The number below the bar is called denominator: 200
The fraction bar means that the two numbers are dividing themselves.
To get fraction's value divide the numerator by the denominator:
Value = 4,855 ÷ 200
To calculate the greatest common factor, GCF:
1. Build the prime factorizations of the numerator and denominator.
2. Multiply all the common prime factors, by the lowest exponents.
Factor both the numerator and denominator, break them down to prime factors:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
4,855 = 5 × 971;
4,855 is a composite number;
In exponential notation:
200 = 2 × 2 × 2 × 5 × 5 = 23 × 52;
200 is a composite number;
Mr. Chu is slicing for cantaloupes his for his class there are 24 students in the class if Mr. Chu cuts the cantaloupes to make a equal portion for each student how many of the whole cantaloupe what each student get
Answer:
3 cantaloupes
Step-by-step explanation:
Since there are 24 students if you divide 24 by 3 it equals 8 so eat cantaloupe should be cut into 8 pieces. So, Mr.chu should buy 3 cantaloupes and cut each of the cantaloups in 8 equivalent slices for the students.
Estimate 95.63+66.552 by first rounding each number to the nearest whole number
Answer:
162
Step-by-step explanation:
95.63 rounds up to 96
66.552 stays at 66
96+66=162
can you please help me with this?
Answer:
B?
Step-by-step explanation:
I beilieve its B? Ive never heard about dances for inuguration.
how do you solve -5 ( -6 - 3x) + 8 = 83
Answer:
x=3
Step-by-step explanation:
-5(-6-3x)+8=83
Distribute the -5 to both terms in the parentheses by multiplication, multiply the -5 by the -6 and the -3x.
30+15x+8=83
Add like terms, add the 30 and the 8.
38+15x=83
Subtract 38 from both sides to isolate the x on the left side.
15x=45
Divide by 15 on both sides to solve for x.
x=3
The total surface area of this cuboid is 76 cm.
Find the value of x.
x cm
4 cm
5 cm
Answer:
76×5+4
380+4=384
Please help me with this question