For the given expressions , the equivalent expressions are as follow:
9 to the fourth power9•9.9•99⁴As given in the question,
Given expressions are given below:
9 to the fourth power369•9.9•94 to the ninth power9⁴Simplify and find the equivalent expression from the following given expressions:
9 to the fourth power=9⁴
= 9 × 9 × 9 × 9
= 6561
3636 = 6²
≠ 6561
9•9.9•9=9⁴
= 9 × 9 × 9 × 9
= 6561
4 to the ninth power= 4⁹
= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
=262144
≠6561
9⁴= 9⁴
= 9 × 9 × 9 × 9
= 6561
Therefore, for the given expressions , the equivalent expressions are as follow:
9 to the fourth power9•9.9•99⁴The complete question is :
Which expressions are equivalent? Choose ALL that apply.
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A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5. What is the length of the third side of the triangle?
x + 13
2x + 13
5x − 5
12x + 3
The length of the third side of the triangle is 2x+13.
According to the question,
We have the following information:
A triangle has a perimeter of 7x + 8. The first side of the triangle has a length of 3x, and the second side has a length of 2x − 5.
We know that perimeter of triangle is the sum of all three sides of triangle.
Let's take its third side to be y.
So, we have the following expression:
3x+2x-5+y = 7x+8
5x-5+y = 7x+8
Adding 5 on both the sides:
5x+y = 7x+8+5
5x+y = 7x+13
Subtracting 5x from both the sides:
y = 7x-5x+13
y = 2x+13
Hence, the correct option is B.
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Answer:
B. 2x+13
Step-by-step explanation:
I got it right on the test
a certain type of equipment is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. how is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
According to the central limit theorem, given a population with mean μ and standard deviation σ, if a suitably large random sample (n ≥ 30) is drawn from the population with permutation, the distribution of the sample mean will be approximately normally distributed. Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.
Then the mean of the sample mean is given by
[tex]\mu_ {x} =\mu[/tex]
and the standard deviation of the sample mean is given by
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]
The standard deviation of the sample mean is inversely proportional to the sample size n
so if n increases, the standard deviation decreases and vice versa.
(a) Sample size increased from 64 to 196.
As mentioned above, the standard deviation decreases as the sample size increases.
Therefore, increasing the value of n from 64 to 196 reduces the standard deviation of the sample mean.
n = 64 sample mean standard deviation:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{64} } \\\\\sigma_{x} = 0.7[/tex]
n = 196 sample mean standard deviation:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{196} } \\\\\sigma_{x} = 0.4[/tex]
sample mean standard deviation decreased from 0.7 to 0.4 n was 64 When it increased to 196.
Therefore the variance is also decreases.
(b)
decreace the sample size, increase the standard deviation.
Therefore, as the value of n decreases from 784 to 49, the standard deviation of the sample mean increases.
Standard deviation of sample mean for n = 784:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{784} } \\\\\sigma_{x} = 0.2[/tex]
Standard deviation of sample mean for n = 49:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{49} } \\\\\sigma_{x} = 0.8[/tex]
Standard deviation of sample mean increased from 0.2 to 0.8 while, n increased from 784 Then 49 decreases.
Therefore, the variance is also increases.
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Mrs. Dellett took up archery as a hobby. On her first attempt, she only scored 18 points.
Every attempt after that, she increased her score by 24 points. How many points did she score on her 9th attempt?
OA. 24
OB. 198
O C. 200
OD. 210
The points scored by Mrs. Dellett on her 9th attempt is 210.
Given, Mrs. Dellett took up archery as a hobby.
On her first attempt she scored 18 points.
then every attempt after that, she increased her score by 24 points.
first attempt = 18 points
after this her score increased to 24 points on every attempt.
second attempt = 18+24 = 42
third attempt = 42+24 = 66
fourth attempt = 66+24 = 90
fifth attempt = 90 + 24 = 114
sixth attempt = 114 + 24 = 138
seventh attempt = 138 + 24 = 162
eight attempt = 162 + 24 = 186
ninth attempt = 186 + 24 = 210
Hence the option D is correct.
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Please help me Find the slope of the line
Answer:
Step-by-step explanation:
d- down four then right three
A taxi ride cot a cutomer a total of \$13. 73$13. 73dollar ign, 13, point, 73, which included 4\%4%4, percent ale tax and then a \$1$1dollar ign, 1 urcharge. What wa the ubtotal before the urcharge and ale tax?
The subtotal before the surcharge and the sales tax is $12.25 .
In the question ,
it is given that ,
the total amount paid for the taxi ride = $13.73
sales tax percent charged = 4%
amount of surcharge = $1 .
let the subtotal before the tax and surcharge be "x"
the amount paid by the customer can be represented by the equation ,
total amount = cost + 4% of cost + surcharge
Substituting the values from above , we get
13.73 = x + 4% of x + 1
4% of x + x = 13.73 - 1
0.04x + x = 12.73
1.04x = 12.73
x = 12.73/1.04
x = 12.24038
x ≈ 12.25
Therefore , The subtotal before the surcharge and the sales tax is $12.25 .
The given question is incomplete , the complete question is
A taxi ride cost a customer a total of $13. 73, which included 4% , percent sales tax and then a $1dollar surcharge. What was the subtotal before the surcharge and sales tax ?
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the population of a city increases by 4,000 people each year. in 2005 the population is projected to be 450,000 people. what is an equation that gives the city's population p (in thousands of people) x years after 2010
Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
As given in the question,
Let 'p' represent the population in thousands of people.
Let x represents the number of years.
Population projected in 2005 = 450,000 people
= 450 ( in thousand people)
Population increases by 4000 people each year that is equal to 4 (in thousand of people)
Required equation to represent the population in x years ( in thousand of people ) is given by:
p = 4x + 450
Population in 2010 is equal to :
p = 4 ( 2010 - 2005) + 450
= 4(5) + 450
= 20 + 450
= 470 ( in thousand of people)
= 470,000 people
Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.
Total population in 2010 is equal to 470,000 people.
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A student was asked to name all values of n that make the relation a function. Correct the error.
{(2,8), (6,0), (4,2), (2n,n)}
n can be any value except 2,6, or 4
The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2
What is a function in mathematics?A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.
The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.
The known elements of the set A in the question are; 2, 6, and 4
The elements of the set A are known as the domain of the function.
The known element of the set B are 8, 0, and 2
The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)
To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4
Therefore;
n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2
The correct statement is therefore;
n can be any value except 1, 3, or 2
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find x, y and z HELPSS mathh
Answer:
[tex]\boxed{\sf y=37^o}[/tex]
[tex]\boxed{\sf x=74^o}[/tex]
[tex]\boxed{\sf z=25^o}[/tex]
Step-by-step explanation:
Let's first solve for y:-
*Linear pairs are supplementary angles, meaning there sum should be 180° *
[tex]\sf 2y^o+106^o=180^o[/tex]
[tex]\sf 2y=180-106[/tex]
[tex]\sf \cfrac{2y}{2} =\cfrac{74}{2}[/tex]
[tex]\boxed{\sf y=37^o}[/tex]
*Consecutive angles are also supplementary angles = 180°*
[tex]\sf x=2y[/tex]
[tex]\sf x=2(37)[/tex]
[tex]\boxed{\sf x=74^o}[/tex]
By corresponding angles,
[tex]\sf 4z+6=106[/tex]
[tex]\sf 4z+6-6=106-6[/tex]
[tex]\sf \cfrac{4z}{4} =\cfrac{100}{4}[/tex]
[tex]\boxed{\sf z=25^o}[/tex]
_____________________
Hope this helps!
Have a good day!
Use grouping symbols to make each statement true 31.) 25 - 8 x 3 = 51 32.) 9 + 4 x 5 - 3 = 17
Answer:
31. (25 - 8) x 3 = 51
32. 9 + 4 x (5 - 3) = 17
Step-by-step explanation:
grouping symbols
31.) 25 - 8 x 3 = 51
(25 - 8) x 3 = 51
Do the parentheses first
17 * 3 = 51
51=51
32.) 9 + 4 x 5 - 3 = 17
9 + 4 x (5 - 3) = 17
Parentheses first
9 + 4 * 2 = 17
Multiply
9+8 = 17
Add
17=17
Philip buys a car from a friend and will pay his friend
the same amount of money each month until the car
is paid for. The following graph and table give the
amount of money in dollars Philip owes his friend, as
a function of the amount of time in months. which of the following conclusions could be made from this functional relationship?
Jaylan makes limeade using
3
4
cup water per
1
5
cup lime juice. Wanchen makes limeade using
3
5
cup water per
1
2
cup lime juice. Find the unit rates of water (cups) per lime juice (cups). Whose limeade has a weaker lime flavor? Enter your answer as a proper fraction or a mixed number. jaylans contains how many cups of water per lime juice
The unit rate of the number of cups of water per cup of lime juice are;
Jaylan;
Unit rate is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juiceWanchen;
Unit rate is 2.91.[tex]\overline {6}[/tex] cups of water per cup of lime juiceWhat is a unit rate?Unit rate indicates the rate of an item for a quantity of one of another item such that when the quantitative relationship is expressed as a ratio, the denominator will be one.
The content of limeade Jaylan makes are;
34 cup water for every 15 cup lime juiceThe ingredient of the limeade Wanchen makes are;
35 cups of water per 12 cups of lime juiceThe unit rate of water (cups) per lime juice (cups) is therefore;
Jaylan; 34 cups of water for every 15 cups of lime juice
Therefore;
34/15 cups of water for 1 cup of lime juice
34/15 = 2.2[tex]\overline 6[/tex]
The unit rate of the drink Jaylen makes is 2.2[tex]\overline 6[/tex] cups of water per cup of lime juice
Wanchen; 35 cups of water per 12 cups of lime juice
Therefore;
35/12 cups of water per cup of lime juice
35/12 = 2.91[tex]\overline{6}[/tex]
The unit rate is 2.91[tex]\overline 6[/tex] cups of water per cup of lime juice
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1. A car is 180 inches long. A truck is 90% longer than the car. How long is the truck?
€ 1611
Sund 19 x6m 19rito
lliw doum wodazis1 101A
A. 162 inches
B. 260 inches
sing erit, fi joi ysą of Inow ode nodW SS2 is bssing aaw tedi allendmu ns triguod
101
esw isdi
C. 342 inches
Azi xst 29162 TOP vd batnyp
went Christmas shopping. Her total was $150. She has a coupon for 40%
D. 360 inches
Stavoms Inuopeib 19d asw fedW
1sdW s
Using the percentage, the truck is 342 inches long. So the option C is correct.
In the given question we have to find the length of the truck.
As given that, a car is 180 inches long.
A truck is 90% longer than the car.
The length of the car is 180 inches.
Truck is longer than the cars is 90%.
So the length of the truck = 180+180*90%
The percentage represent in the ratio of 100.
So the length of the truck = 180+180*90/100
Simplifying
The length of the truck = 180+162
The length of the truck = 342
Hence, the truck is 342 inches long. So the option C is correct.
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the time to complete a bridge varies inversely with the square root of the number of people working. if 9 people can complete the job in 75 days then how long would it take 25 people?
If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.
Let T be the time and L be the Labor (Number of people working on the bridge).
T ∞ 1/√L (Inverse relationship)
T = K/√L ----------------------------- (1)
Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.
According to the question,
Time (T) = 75 days and
labor (L) = 09
From the equation (1), we get,
T = K / √L
⇒ 75 = K/√9
⇒ 75= K/3
⇒ K= 225
First, the relationship between these variables is:
T = 225/√L
Therefore, how long it will take 25 people to do it means that we should look for the time.
T=225/√L
⇒ T= 225/√25
⇒ T= 225/5
⇒ T= 45 days.
therefore, 25 people needs 45 days to complete the job.
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4) A pizza shop sells pizzas that are 12 inches (in diameter) or larger. A 12 inch cheese pizza costs $9. Each additional inch costs $1.75, and each additional topping costs $0.50. Write an equation that represents the cost of a pizza. Be ure to specify what the variables represent.
The equation to represent the cost is C = 8 + 1.50x + 0.75y.
To write an equation that represents the cost of a pizza.
An equation that represents the cost of a pizza will be
C = 9 + 1.75x + 0.50y
Fixed cost = $9
Cost of additional inch = 1.75x
Cost of additional topping = 0.50y
Total cost (C) will then be:
= 9 + (1.75 × x) + (0.50 × y)
C = 9 + 1.75x + 0.50y
Hence the answer is, the equation to represent the cost is C = 8 + 1.50x + 0.75y.
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A certain fraction, if reduced, is equal to ⅘. If 3 is added to the numerator, the new fraction is equal to 1. What is the fraction?
Let x = numerator
Let y = denominator
Answer: x = 12, y = 15
Step-by-step explanation: 12/15 reduces to 4/5 because 12 divided by 3 is 4 and 15 divided by 3 is 5. 12 + 3 is 15 so if you add 3 to the numerator, you get 15/15, which is equal to 1.
(3s+2f=18)
(2s+3f=15.75)
Answer:
(s, f) = (4.5, 2.25)
Step-by-step explanation:
You want the solution to the simultaneous equations ...
3s+2f = 182s+3f = 15.75SolutionWriting these in general form, we have ...
3s +2f -18 = 0
2s +3f -15.75 = 0
Using the "cross-multiplication method" for solution, we find ...
∆1 = (3)(3) -(2)(2) = 5
∆2 = (2)(-15.75) -(3)(-18) = 22.5
∆3 = (-18)(2) -(-15.75)(3) = 11.25
s = ∆2/∆1 = 22.5/5 = 4.5
f = ∆3/∆1 = 11.25/5 = 2.25
The solution is (s, f) = (4.5, 2.25).
__
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Annika’s older sister cousin borrowed 800$ to repair her car she will pay off the loan after 2years by paying back the principal plus 4.5% simple interest for each year. How much will she pay in interest?
Answer:
Step-by-step explanation:
she will pay $80 in interest.
If you roll a die three times, how many different sequences are possible? a. 6 cubed = 216 b. 3 superscript 6 baseline = 216 c. 3 superscript 6 baseline = 729 d. 6 cubed = 729
Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex] =216
What is outcome of an event?
Suppose an event is happening. The result of the event is called outcome of the event.
For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die
Number of outcomes of rolling a die first time = 6
Number of outcomes of rolling the die second time = 6
Number of outcomes in rolling a die third time = 6
Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]
= [tex]6^3[/tex]
= 216
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Solve the equation or formula for the variable indicated.
X-2y=1
Answer:
Step-by-step explanation:
-2y = -x -1
2y = x+1
y = 1/2x+1/2
The rectangular floor of a classroom is 26 feet in length and 28 feet in width. A scale
drawing of the floor has a length of 13 inches. What is the perimeter, in inches, of the
floor in the scale drawing?
Situation:
A farmer in China discovers a mammal
hide that contains 30% of its original
amount of C-14.
N = Noe-kt
No inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k
= 0.0001
t = time, in years
Find the age of the mammal hide to the
nearest year.
Enter the correct answer.
DONE
The age of the mammal is 3567 years.
Change the given numbers' letters in the equation to match:
N ="NOekt"
N-amount following t years
If not, the initial sum
K=0.0001t, where t=the number of years
Change the given numbers' letters in the equation to match:
0.70 = 1 * e^-0.0001t
Consider the two sides' logarithms:
t = -0.1549 / (-0.0001 * 0.43429) log0.70 = loge-0.0001t -0.1549 = -0.0001t * 0.43429 t = 3566.74
The age is 3,567 years, rounded to the nearest year.
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pls give answer pls pls
Answer:
k = 13
Hope this helps : )
Step-by-step explanation:
To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.
1. Divide 7 on both sides of the equal sign.
7k = 91
7 7
2. Answer.
The 7 cancels out so we are left with k = 13 since
91 ÷ 7 = 13
k = 13
3. Check.
Plug in the variable "k."
7(13) = 91
91 = 91 ✓
a multiple choice test consists of six questions, each of which has five choices. each question has exactly one correct answer. william guesses randomly at each answer. what is the probability that he gets four or fewer questions correct? (round your answer to four decimal places.)
The probability that he gets four or fewer questions correct is 0.9984
Let p be probability of getting correct answer and q be probability of getting in correct answer.
Number of trails : n = 6
Number of Successes : x = 4
By using binominal distribution ,
P(x≤4) = 1 - P(x>4)
= 1 - [P(x = 5) + P(x = 6)]
= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]
solving combination ,
= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]
= 1 - (24 + 1 / 625)
= 1 - 25 / 625
= 624/625 = 0.9984
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[tex]\frac{x}{3}[/tex]=4.5
Answer:
Step-by-step explanation:
Ok:
1. First write as equation!
x/3=4.5
2. Isolate the variable on the left side. Remember if a variable or number goes over equal sign, it becomes opposite
x/3=4.5
x=4.5*3
x=13.5
3. Double Check as always!!
13.5/3= 4.5
TRUE
Answer: 13.5
Answer:
13.5 is the answer ..hopefully this helps
x² - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Show your working
Answer
Answer:
16.2
Step-by-step explanation:
16.18034 to 1 decimal place = 16.2
If it 2 decimal place =16.18
Cristian put a large rock on the bottom of the terrarium he made for his pet turtle. The rock is a right rectangular prism 10cm wide by 12 cm long. The rock displaces 1800cubed (3)
How high is the rock?
The height of the block that has dimensions of 10 cm and 12 cm and a volume of 1,800 cubic centimeters is 15 cm
What is the volume of a rectangular prism?A rectangular prism is a figure that has six faces that are rectangles.
The dimensions of the rock are;
Width of the rock = 10 cm
Length of the rock = 12 cm
Volume displaced by the rock = 1,800 cubic centimeter
Height of the rock = Required
Let h represent the height of the rock, we get;
Volume of a rectangular prism, V = Length × Width × Height
Volume of the rock = 10 × 12 × h = 1,800
h = 1,800 ÷ (10 × 12) = 15
Where the volume of the rock is 1,800 cubic centimeter, the height of the rock is 15 centimeters
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Mrs Tan worked at a jewellery shop and sold a gold bracelet. If she wanted to make a profit of 52%, she would need to sell the bracelet at $1216. How much profit would she get if she sold it at $2012?
If she sold the gold bracelet at $2012, the profit would be $1212
Let original price of the gold bracelet be x
Mrs Tan wanted to make a profit of 52%
The selling price would be $1216
Selling price = x + 52% of x
1216 = x + (52/100)x
1216 = 152/100x
x = 1216(100/152)
x = 800
The original price is $800
The price at which she sells the gold bracelet is 2012
Profit = selling price - original price
= 2012 - 800
= 1212
Therefore, if she sold the gold bracelet at $2012, the profit would be $1212
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Jina is riding on a bike course that is 40 miles long. So far, she has ridden 16 miles of the course. What percentage of the course has Jina ridden so far?
Answer:40%
Step-by-step explanation: Take 16 divided by 40 and you get .04, which equals 40 percent. Another way to think about it is this way: if 40 miles is the total distance, every 4 miles is 10% of the total. So 16 has to be 40%.
2. A line goes through the points (2,10) and (-2,4).
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form using the point (2, 10). Show your work.
(c) Write the equation of the line in slope-intercept form. Show your work.
The slope of the line is 3/2, Equation of the line in point-slope form ( y - 10) = 3/2 (x-2), and The equation of the line in slope-intercept form
y = (3/2) x - 13
How do you find equation of a line?Using the slope formula, calculate the slope. To find the y-intercept (b), use the slope and one of the points.
Once you know the values for m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to derive the line's equation.
Therefore,
A line goes through the points (2,10) and (-2,4).
Slope = (y2-y1)/(x2 -x1)
= (4 - 10) / (-2 - 2)
= -6/-4 = 3/2
The equation of the line in point-slope form using the point (2,10)
Slope = 3/2
equation of the line in point slope form :
(y - y1) = m (x -x1)
(y - 10) = 3/2 (x-2)
y = mx + c
Simplifying the above equation, then we get
2 = 3/2 × 10 + c
c = 2 - 15
c = -13
equation of the line is
y = (3/2)x - 13
2y = 3x - 26
the slope-intercept equation of the line
y = (3/2) x - 13
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e trigonometry to work out the size of
angle x.
Check the picture below.
[tex]tan(x) =\cfrac{\stackrel{opposite}{10}}{\underset{adjacent}{4}}\implies tan(x)=\cfrac{5}{2}\implies x=tan^{-1}\left( \cfrac{5}{2} \right)\implies x\approx 68.20^o[/tex]
Make sure your calculator is in Degree mode.