Step-by-step explanation:
2³×2^n+2=32
2^3+n+2=2⁵
n+5=5
n=0
[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{ANSWER:}[/tex]
[tex]\tt n = 0[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]
[tex]_____________________________________[/tex]
[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]
[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]
[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]
When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula f(t)=0.9t^3−0.6t^0.5+10, where t is the time in hours after 6 AM and f(t) is the number of barrels of fuel oil. Step 1 of 3 : How much fuel is consumed by 11 AM? Round your answer to 2 decimal places.
Step-by-step explanation:
the answer is in the image above
The amount of oil consumed in 5 hours is 120.5 barrels.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, of fuel consumption in a factory from 6 am to 6 pm,
The equation =
f(t) = 0.9t³-0.6[tex]t^{0.5}[/tex]+10
where t is the time in hours after 6 am and f(t) is the number of barrels of fuel oil.
We need to find the how much oil is consumed by 11 am,
So, the hours between 11 am to 6 am = 11-6 = 5 hours
So, we need to find the oil consumption in 5 hours, so for the same put t = 5, in the equation,
f(5) = 0.9(5)³-0.6[tex](5)^{0.5[/tex]+10
= 112.5-2+10
= 120.5
Hence, the amount of oil consumed in 5 hours is 120.5 barrels.
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Assessment
Cymraeg
Isaac plans a hidden treasure game.
Treasure is hidden under the sand in a tray. The tray for the sand is a cuboid: 0.8 m long,
0.6 m wide and 0.1 m deep. Sand comes in 25 kg bags with an approximate volume of
17,000 cm?
How many bags must Isaac buy to completely fill the tray?
3
Isaac needs to buy
bags of sand.
2
Answer:
So, to fill the tray completely , he needs 3 bags of sand.
Step-by-step explanation:
Tray dimensions,
length = 0.8 m
Width = 0.6 m
height = 0.1 m
Volume of one sand bag = 17000 cm^3
Let the volume of the tray is V.
V = length x idth x height
V = 0.8 x 0.6 x 0.1 = 0.048 m^3
Number of sand bags
[tex]n=\frac{0.048}{17000\times 10^{-6}}\\\\n = 2.82[/tex]
So, to fill the tray completely , he needs 3 bags of sand.
5a + 4b = 31
5a + 6b = 39
What is a and what is b
Answer:
a = 3 and b = 4
Step-by-step explanation:
5a + 4b = 31 --(1)
5a + 6b = 39 --(2)
(2) - (1) : 2b = 8
b = 4 -- (3)
Substituting (3) into (1),
5a + 16 = 31
5a = 15
a = 3 -- (4)
Therefore, a = 3 and b = 4
If this helps you please mark brainliest!
Have a nie day!
A company manufactures two products. Market research and available resources require the following
constraints:
• The number of units of product A manufactured, 2, is at most 500 units more than twice the number
of units of product B. y.
• The square of the company's profit is equal to the sum of 35 times the number of product A units
sold and 50 times the number of product B units sold.
If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these
constraints?
will give brainliest + 50 points :)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of product A and y represent the number of product B, hence:
x ≤ 500 + 2y (1)
Also:
35x + 50y > 22500² (2)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
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ABCD is a kite, so AC DB and DE = EB. Calculate the length of AC, to the nearest tenth of a centimeter.
9514 1404 393
Answer:
AC ≈ 6.8 cm
Step-by-step explanation:
For legs a and b of a right triangle with hypotenuse c, the Pythagorean theorem tells us ...
a = √(c² -b²)
Using this relation, we can find legs CE and AE.
CE = √(3² -2²) = √5
AE = √(5² -2²) = √21
AC is the sum of these two lengths:
AC = AE +EC = √21 +√5
AC ≈ 6.8 cm
I need the answer plzzzzzz
Answer:
answer is 0 in the ones column
No link please
Ergent
Using matrix method solve
the following simulaneous equatin
2x+3y=9
3x-1y=3
Step-by-step explanation:
here are the matrices you were looking for
How do I solve this and answer?
Step-by-step explanation:
at first solve first triangle with Pythagorean solving witch it c²=a²+b²
you have to change a bit so it will be c²-b²=a²
you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²
Part A: Factor x2b2 − xb2 − 6b2. Show your work.
Part B: Factor x2 + 4x + 4. Show your work.
Part C: Factor x2 − 4. Show your work
Answer:
A.2b2(x2-x-3)
B.x2+2x+2x+4
=x(x+2)+2(x+2)
=(x+2)(x+2)
C.x2-2^2
=(x+2)(x+2)
Instructions: Find the value of x
I’ll mark brainliest please help
The little lines theu each section are telling you all those sections are identical, which mean they are the same length.
You are told one section is 10, which means x is also 10
X = 10
Can someone answer with steps and explanation? Thanks.
Answer:
A dilation by a factor of three about Point T followed by a translation of two units downwards.
Step-by-step explanation:
When transforming functions, we will reflect/dilate the figure first and then translate it. This is directly from the order of operations.
Since we are trying to determine the transformation that was performed, we can try to map ΔS'T'U' onto ΔSTU. We can start by translating the figure and then determining any reflections/dilations.
First, we can translate ΔS'T'U' up two units to map T' onto T. This is represented by the black triangle in the image below. Let the black triangle be ΔS''T''U''. (T'' and T are the same point.)
Next, notice that from Point T'' to U'', we move nine units right and six units up.
From Point T to Point U, we move three units right and two units up.
Likewise, from Point T'' to S'', we move six units left and nine units up.
From Point T to Point S, we move two units left and three units up.
Therefore, to map ΔS''T''U'' onto ΔSTU, we dilate ΔS''T''U'' about Point T by a factor of 1/3.
Hence, by reversing the transformations, to acquire ΔS'T'U', we can see that we will dilate ΔSTU by a factor of three about Point T and then a perform a translation of two units downwards.
PLEASE HELP WILL MARK YOU!
It says:state whay additional information is required in order to know that the triangles are congruent for the reason given
This is pt.1
Step-by-step explanation:
12) ASA - we need the second angle.
13) We need the side and second angle.
14) We need second side. First side we know is equal since both triangles share it.
he Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and the Reputation of the Company for over world-wide corporations. Both the Quality of Management and the Reputation of the Company were rated on an Excellent, Good, and Fair categorical scale. Assume the sample data for respondents below applies to this study. Excel File: data12-13.xlsx a. Use level of significance and test for independence of the quality of management and the reputation of the company. Compute the value of the test statistic (to 2 decimals). Do not round intermediate calculations. The -value is - Select your answer - What is your conclusion? - Select your answer - b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
[tex]H_0:[/tex] Management quality and corporate reputation are independent.
[tex]H_1:[/tex] Management quality and corporate reputation are not independent.
Test statistic:
[tex]\to \chi^2 = \frac{\sum (O-E)^2}{E}[/tex]
[tex]= 0.71429 + 0.0102 +2.8809+0.625+1.75 +0.3333 +0+3.2143+7.5\\\\= 17.02806[/tex]
The critical [tex]\chi^2[/tex] for[tex]df = (r-1)(c-1) = (3-1)(3-1)= 4[/tex] and [tex]\alpha = 0.05[/tex] is [tex]\chi^2= 9.4877[/tex]
Test statistic:
[tex]17.02806 > 9.4877[/tex] therefore rejecting the null hypothesis [tex]H_0[/tex].
p-value[tex]= 0.001909[/tex]
Interpretation:
There is no internal governance quality as well as the reputation of the organization.
A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 13 days. Estimate the percentage of the original amount of the isotope released by the explosion that remains 6 days after the explosion.
Answer:
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Step-by-step explanation:
The following formula can be utilized for this question:
[tex]N = N_o (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\\frac{N}{N_o} = (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\[/tex]
where,
[tex]\frac{N}{N_o}[/tex] = ratio of the remaining amount to the original amount = ?
t = tme passed = 6 days
[tex]t_{1/2}[/tex] = half-life = 13 days
Therefore,
[tex]\frac{N}{N_o} = (\frac{1}{2} )^{\frac{6\ days}{13\ days} }\\\\[/tex]
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Based on the Pythagorean theorem , find the missing length for each of the given right triangles
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the right trianglea are not given. The general explanation is as follows.
Using Pythagoras Theorem, we have:
a² = b² + c²
Where:
a => hypotenuse
Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.
The hypotension becomes
a² = 3² + 4²
a² = 9 + 16.
a² = 25
Take square roots.
a = 5
If any of the other side lengths is missing; you make that side the subject and then solve.
find the volume of the cone 3.4 m x 5.5 m
Answer:
63,5
Step-by-step explanation:
pi r bình pnhân hươnh g
When choosing a four-number PIN.
(personal identification number)
how many different PINS are possible?
(The choice of digits 0-9 are available for each number.)
Answer:
10,000 different PINS are possible
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
Four each digit on the PIN, there are 10 possible outcomes. The digits are independent. So, by the fundamental counting principle:
[tex]T = 10^4 = 10000[/tex]
10,000 different PINS are possible
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Step-by-step explanation:
everything can be found in the picture
4. Solve the following system of equations for x.
2x + 3y = -14
y = 6x + 22
A. X = -2
B. X = 2
C. X = -4
D. X = 4
We are given the system of equations -:
[tex] \large{ \begin{cases} 2x + 3y = - 14 \\ y = 6x + 22 \end{cases}}[/tex]
Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.
[tex] \large{2x + 3(6x + 22) = - 14}[/tex]
Expand 3 in the expression so we can combine like terms and isolate x-variable.
[tex] \large{2x + 18x + 66 = - 14}[/tex]
Then combine like terms.
[tex] \large{20x + 66 = - 14}[/tex]
Get rid of 66 from the left side by subtracting both sides by itself.
[tex] \large{20x + 66 - 66 = - 14 - 66} \\ \large{20x = - 80}[/tex]
To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.
[tex] \large{ \frac{20x}{20} = \frac{ - 80}{20} }[/tex]
Simplify to the simplest form.
[tex] \large{x = - 4}[/tex]
Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.
Answer
x = -4I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!
Answer:
A. x = -2
C. x = -4
Step-by-step explanation:
y = 6x + 22
2x + 3•(6x+22) = -14
20x = - 80
x = -4
y = 6x+22
y = 6(-4)+22 = -2
A rectangular picture is four times as long as it is wide. The area of the picture is 1024 square inches. Find the
dimensions of the picture.
Width = 16 inches, Length = 64 inches
Width = 64 inches, Length = 64 inches
Width = 16 inches, Length = 16 inches
Width = 64 inches, Length = 16 inches

El perro de Antonia debe comer 0,48 kg de alimento cada día. ¿Cuánto alimento necesita para 30 días?
Answer:
Amount of food need for 30 days = 14.4 kilogram
Step-by-step explanation:
Given information:
Amount of food dog eat each day = 0.48 kilogram
Find:
Amount of food need for 30 days
Computation:
⇔ Amount of food need for 30 days = Amount of food dog eat each day x number of days
⇔ Amount of food need for 30 days = 0.48 x 30
Amount of food need for 30 days = 14.4 kilogram
14.4 kilogram is right answer.
It costs $100 to join a fitness center plus a monthly fee you spent $700 last year at the fitness center how much was the monthly fee
Answer:
58.3
Step-by-step explanation:
divide 700 by 12
Answer:
$50
Step-by-step explanation:
The equation for this is:
700 = 12m + 100, where $700 is the total cost, m is the monthly fee, 12 is the number of months in a year, and $100 is the starting fee
Solve the equation:
700 = 12m + 100
12m = 600
m = 50
A rectangle has side lengths (x +5) feet and (2x−3) feet. Write a linear expression in simplest form to represent the perimeter. Find the perimeter if the value of x is 6 feet.
Answer:
6x+4 ft
40 ft
Step-by-step explanation:
The perimeter of a rectangle is
P = 2(l+w)
= 2( x+5 + 2x-3)
Combine like terms
= 2(3x+2)
Distribute
=6x+4
Let x= 6
= 6*6+4
= 36+4
= 40
The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Answer:
a. there could be a problem of high error
b. randomized block design can remove the issue of heterogeneity
c. yes they should
d, yes it could
Step-by-step explanation:
a. if their is a lack of homogeneity among the sample population, then the results that would be obtained are going to be with increased experimental error.
b. given the number of treatment, the randomized block design technique can be done. This would then remove the issue of heterogeneity. It also gives more information and the results from the test are easier. Even in the presence of missing data, the missing plot technique can be employed.
c. when a control group is used, it makes easier the examination of the market research in a more effective way.
d. Yes it could be a double blind one. This would help to take away the problem of bias.
Which ordered pair is a solution to the system of inequalities? y< 3x y< 5
Answer:
Step-by-step explanation:
Split it into two:
Y<3x
Y<5
X = 1
Y = 3
(1,3)
X = 2
Y = 6
(2, 6)
Plot the line up to y = 4.999999999999999999999 and not higher.
Answer:
Plot the line up to y = 4.999999999999999999999 and not higher
A man at ground level measures the angle of elevation to the top of the building to
be 87°. If at this point, he is 20 meters away from the building, what is the height of
the building?
Answer:
The bulding is 381,623 meters high.
Step-by-step explanation:
To dertermine the height of the bulding I would use tanα = rectangulair side / closest rectangulair side.
19,08 = the height/ 20m.
<=> 19,08.20m= the height = 381,623 m
Help please i will mark brainlist !!!!
Answer:
You need to add the numbers up
0.4 +0.2+0.1=0.7
1-0.7=0.3
Ans=0.3
4.27cm rounded to the nearest cm
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]4.27\text{cm} \approx\boxed{4\text{cm}}[/tex]
»»————- ★ ————-««
Here’s why:
We would locate the whole number and look at the number to the right. In this case, we would look at the '2' in the tenths place.Since it is less than or equal to 4, we would round down.⸻⸻⸻⸻
Recall the Rounding Rules:
If the digit to the right is less than or equal to 4, we round down.If the digit is greater than or equal to 5, we round up.⸻⸻⸻⸻
[tex]\underline{4.27cm}\\\\\rightarrow2\leq 4\\\\\boxed{4.27cm \approx 4cm}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Describe and correct the error in finding DC
Answer:
DC = 2
Step-by-step explanation:
The wrong equation was used.
The right equation to use based on the midsegment theorem of a trapezoid is:
MN = ½(AB + DC)
MN = 8
AB = 14
Substitute
8 = ½(14 + DC)
Multiply both sides by 2
8*2 = ½(14 + DC)*2
2*8 = 14 + DC
16 = 14 + DC
16 - 14 = 14 + DC - 14
2 = DC
DC = 2
Q- getting a number greater than 3 or an odd number?
Step-by-step explanation:
So one's chance of getting a number greater than 3 is 3 chances out of 6 numbers that could be rolled or 1/2. Then we determine what the chances are of getting an ODD number. That includes 1, 3, & 5. So one's chance of getting an odd number is 3 chances out of the 6 numbers on the die, which is also 1/2.