1. Simplify by using the distributive property:
4 (2x +9)
Answer:
8x+36
Step-by-step explanation:
Hi, let me help you out!
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In order to simplify this, we should use the Distributive Property:
[tex]\longrightarrow\tt{a(b+c)=ab+ac}[/tex]
According to the property,
[tex]\longrightarrow\tt{4(2x+9)=8x+36}[/tex]
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If you need any explanation or clarification, feel free to reach out! :D
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Which expression is equivalent to 8/9 divided 3/4?
don't feel like using my brain
Answer:
32/27
Step-by-step explanation:
The fractional division is draculated as follows:
(a/b) / (c/d) = (a*d) / (b*c)
then:
(8/9) / (3/4) = (8*4) / (9*3) = 32/27
Can you help me please
Suppose that a population of bacteria triples every hour and starts with 700 bacteria.
(a) Find an expression for the number n of bacteria after t hours.
(b) Estimate the rate of growth of the bacteria population after 1.5 hours.
Answer:
(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
Step-by-step explanation:
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a real positive.
When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.
An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.
In that case, the formula used to model the growth of a population is given by:
P(t)=P0*[tex]a^{t}[/tex]
where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.
In this case:
P0=700a=3Replacing, you get:
P(t)=700*[tex]3^{t}[/tex]
An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
The derivative of this function P (t) is:
n'(t)=700*ln(3)*[tex]3^{t}[/tex]
and reflects the growth rate of the bacteria population.
So, the rate of growth of the bacteria population after 1.5 hours is:
n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]
Solving, you get:
n(1.5)≅ 3,996
The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
please help me with the question.
Answer:
Step-by-step explanation:
∠a is corresponding to ∠f
∠b is alternate interior angle to ∠e
∠g is alternate exterior to ∠d
∠f is vertical to ∠h
∠b is consecutive( same side) interior with ∠f
Ruth's credit card has an APR of 10,91%, and it computes finance charges using the previous balance method on a
30-day billing cycle. During the April billing cycle, she made a $45.17 payment on April 10th and a $88.34 purchase on
April 17th. Her total at the start of May was $847.64. What was her balance at the beginning of April?
a $890.91
b. $797.22
C.$796.87
d. $804.47
Please select the best answer from the choices provided
Answer:
It's B trust
Step-by-step explanation:
The required balance at the beginning of April is $796.87. Option C is correct.
What is interest?Simple interest is defined as the percentage of earnings on the lending for a period of time
To determine Ruth's balance at the beginning of April, we can work backward from her total at the start of May.
Let's call Ruth's balance at the beginning of May "B".
We know that during the April billing cycle:
She made a $45.17 payment on April 10th
She made a $88.34 purchase on April 17th
The APR is 10.91%
So, B = B - $45.17 - $88.34 + (B * 0.1091 * 30 / 365)
Solving for B, we get:
B = $796.87
So, the answer is C. $796.87.
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Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic Ocean. One of the studies involves a random sample of 16 baluga whales. The researchers want to create a 95% confidence interval to estimate the true mean weight of male baluga whales. Their data follow a normal distribution. The population standard deviation of weights of male baluga whales is ????=125 kg, and the researchers feel comfortable using this standard deviation for their confidence interval.
Assuming the relevant requirements are met, calculate the margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean.
a. 15.31 kg
b. 51.40 kg
c. 61.25 kg
d. 80.49 kg
Answer:
c. 61.25 kg
Step-by-step explanation:
The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean.
a. 15.31 kg
b. 51.40 kg
c. 61.25 kg
d. 80.49 kg
Margin of Error Formula= z × Standard deviation/√n
95% confidence interval = 1.96
Standard deviation = 125kg
n = 16 samples
Margin of error= 1.96 × 125/√16
= 1.96 × 125/4
= 245/4
= 61.25kg
The margin of error in estimating the true mean weight of male baluga whales in the Artic Ocean is 61.25kg
An equation is shown. What factor is missing from the equation? 32 + 20= (8+5)*
Answer:
4
Step-by-step explanation:
32+20=52
8+5=13
52/13=4
if u make 120.45 in 15 2/3 hours how long did u work if u made 40.15 ?
Answer:
about 5.22hrs
Step-by-step explanation:
cross multiply
120.45 ?
15.67 40.15
120.45*40.15
=629.1505
629.1505/15.67
=5.2233333...
What are the steps in solving the equation 4(2x + 3) = 10x?
Answer:
Step-by-step explanation:
Distributive property, subtraction, division
4(2x + 3) = 10x
8x + 12 = 10x
12 = 2x
6 = x
Evaluate this expression when p = 4 and q = -2:
4(√p+q²)
A. 4
B. -8
C. 12
D. 24
Answer:
24
Step-by-step explanation:
Find the missing angle. solve for ?
PLZ HELP =<
Answer:
70 degrees
Step-by-step explanation:
180-120=60
180-(60+50)=70
Write a minimum 100-word essay on how you can currently use and may use your knowledge and skills of rotations and it's use in digital technology. (WILL MARK BRAINLIEST!! NO SILLY ANSWERS PLS)
The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $633 and standard deviation σ = $45.
Required:
a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)
Answer:
a) 0.4121
b) $588
Step-by-step explanation:
Mean μ = $633
Standard deviation σ = $45.
Required:
a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
We solve using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x = $646
z = 646 - 633/45
z = 0.22222
Probability value from Z-Table:
P(x<646) = 0.58793
P(x>646) = 1 - P(x<646) = 0.41207
≈ 0.4121
b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)
Converting 0.16 to percentage = 0.16 × 100% = 16%
The z score of 16%
= -0.994
We are to find x
Using z score formula
z = (x-μ)/σ
-0.994 = x - 633/45
Cross Multiply
-0.994 × 45 = x - 633
-44.73 = x - 633
x = -44.73 + 633
x = $588.27
Approximately to the nearest dollar, the amount should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16
is $588
1. Using powers of 10, which would be the best choice for the first number to subtract in the division problem 956 ÷ 87?
Answer:
not sure i it is one of these answers but if so , it d
Step-by-step explanation:
When performing division by repeated subtraction method, an equal
amount is subtracted from the dividend several times.
The best choice for the first number to subtract is the the option; 870
Reasons:
Dividing 956 by 87 and subtracting 10 each time, by subtracting 10 87 times gives;
956 - 87 × 10¹ = 86
From which we get;
[tex]\hspace {15} 10\\87| \overline{956}\\\hspace{15in.....} \overline{870}\\\hspace {120in......} 86[/tex]The 870 which is the part product is subtracted first to get a remainder of
86 which is less than 87.
Therefore; using powers of 10, the best choice for the first number to
subtract in the division problem 956 ÷ 87 is 87 × 10 = 870.
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A fair 66-sided die is rolled 77 times and the resulting sequence of 77 numbers is recorded. A) How many different sequences are possible?B) How many different sequences consist entirely of even numbers? C) How many different sequences are possible if the first, third, and fourth numbers must be the same? D) How many sequences are there where every number is different? E) How many sequences are there where there are at least two numbers that are the same?
Answer: A. 279936 sequences.
B. 2187 sequence.
C. 7776 sequence.
D. 46656 sequence
E. 64 sequence.
Step-by-step explanation:
Given data:
A 6 sided fair die
No of time rolled = 7
Resulting sequence recorded = 7.
Solution.
A.) No of different possible sequence
= 6^7
= 279936 sequences.
B.) Sequence consisting of only even number
= there are 3 even numbers between 1 and 7 ( 2,4,6).
= 3^7
= 2187 sequence.
C.) possible sequences are when the first, third, and fourth numbers must be the same.
= 6* 6 ^n
where n = 4
= 6*6^4
= 7776 sequence.
D.) sequence when every number is different.
There are 6 sides of a die, so when every number is different it is.
= 6^6
= 46656 sequence
E.) sequence when atleast there are two numbers that are the same.
= 2^6
= 64 sequence.
What is the total amount, including interest, that the shoe store must pay on the loan? (2 points)
Answer:
2550
Step-by-step explanation:
Hope This Helps
Answer:
2550
Step-by-step explanation:
what dose 3, 3 in the table indicate??? plzzz helppppp
Step-by-step explanation:
it indicates f(x) and g(x)
Answer:
3,3 is a placment in a graph
Step-by-step explanation:
Miss Kito is building a rectangular pen for her lea.She will use the side of her house for one wall of the pen;therefore she will not need any fencing on that side.On the other three sides, she will use special fencing that costs $12 per foot . She wants the entire enclosed area to be 2400 square feet. Lastly,she needs four corner that costs $5 each ?
Let x represent the length of each side of the pen perpendicular to the house and let y represent the length of the side of the pen parallel to the house.Write a function c(x) for the cost of the materials for the llama pen in terms of x. Simplify
Please explain and thank you
Answer:
The answer is "[tex]=24x+ \frac{28800}{x}+20[/tex]"
Step-by-step explanation:
The perimeter of the fence [tex]=2x+y[/tex]
cost of fence[tex]=12(2x+y)[/tex]
cost of corner ports[tex]= 4 \times 5=20[/tex]
cost of pen[tex]= 24x+12y+80.............(1)[/tex]
area of pen[tex]=2400[/tex]
[tex]xy=2400\\\\y=\frac{2400}{x}[/tex]
cost c(x)[tex]=24x+ \frac{12 \times 2400}{x}+20[/tex]
[tex]=24x+ \frac{28800}{x}+20[/tex]
An auto mechanic earns $498.75 in 35 hours during the week. His pay is 2.50 more per hour on the weekends. If he works 6 hours on the weekend in addition to 35 hours during the week,hiw much does he earn
Answer:
Total pay= $599.25
Step-by-step explanation:
First, we need to calculate the unitary pay per hour:
Unitary pay= 498.75/35
Unitary pay= $14.25
Now, we can determine the total earn of 35 regular hours and 6 weekend hours:
Total pay= 498.75 + (14.25 + 2.5)*6
Total pay= 498.75 + 100.5
Total pay= $599.25
Find the area of the triangle whose one angle measure is 55°, the other angle is a right angle and the side opposite the 55° angle is 15 units.
Answer:
Step-by-step explanation:
Area of the right angles triangle will be expressed as;
Area of a triangle = 1/2base * height
Let the height of the triangle be 15 units
Get the base;
The base will be the adjacent;
Using the TOA trig identity;
tan 55 = opp/adj
tan 55 = 15/adj
adj = 15/tan 55
adj = 15/7.42
adj = 2.022 units
Area of the triangle = 1/2 * 15 * 2.022
Area of the triangle = 15 * 1.011
Area of the triangle = 15.165units²
A coat discount 40% off it's regular price. Which value is equivalent to 40%
If you can answer my riddle I will mark as brainlest ok?
RIDDLE: If you give me food I will live but if you give me water I will die. What am I?
Answer:
fire
Step-by-step explanation:
if you give fire food or fuel it will still be alive
but if you give it water it will go out
PLZ GIVE BRAINLEST
Answer:
The answer is a fire because if you put water on a fire, it will die out, but if you put stuff in the fire it will live on.
Please help!!!!
(Show work if possible)
-a^2b^2c^2(a+b-c) find the product
Answer:
-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3
I hope it will be useful.
Solve for h: h + 4.18 = 19.74
An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge. 16 ounces = 1 pound. 2,000 pounds = 1 ton. If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton?
fill in thw blanks please extra points:)
Answer:
First blank- 32000 ounces
Second blank- 2000 pounds
Yes the bridge can hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
16 ounces = 1 pound
32000 ounces = x pounds
==> = 32000/16 = 2000 pounds
2000 pounds = 1 ton
therefore the bridge holds 1 ton
Answer:
First blank- 32000 ounces
Second blank- 2000 pounds
Yes the bridge can hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
16 ounces = 1 pound
32000 ounces = x pounds
==> = 32000/16 = 2000 pounds
2000 pounds = 1 ton
therefore the bridge holds 1 ton
Find the measure of each angle
Answer:
All the work and answer is on the screenshot I have attached.
Step-by-step explanation:
Researchers are interested in assessing if there is an association between dietary cholesterol intake and high blood pressure. The following data was summarized:
Blood Pressure
Dietary Cholesterol High Low Total
High 159 91 250
Low 78 172 250
Total 237 263 500
Required:
a. Estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol.
b. Compute an estimate of the odds ratio of high blood pressure for the two groups
c. Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
Answer:
A) Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) The odds ratio shows that BP is directly proportional to Dietary cholesterol
Step-by-step explanation:
A) estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol
Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) Compute an estimate of the odds ratio of high blood pressure for the two groups
High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
The odds ratio shows that BP is directly proportional to Dietary cholesterol as seen in the the odds ratio that ratio between High BP and High Dietary cholesterol is higher than other odds ratios
What type of transformation has occurred?
A Translation
B Dilation
C Reflection
D Rotation
Answer:
B dilation
Step-by-step explanation:
the shape didnt move but it got bigger