(–0.2b^6)^3(5b) this is the question to be answered
Final answer:
The simplified form of the expression [tex](-0.2b^{6})^3(5b)[/tex] is [tex]-0.04b^{19}[/tex], obtained through raising to a power and multiplication.
Explanation:
The student's question involves simplifying an algebraic expression by raising a term to a power and then multiplying it by another term. To simplify [tex](-0.2b^{6})^3(5b)[/tex], we must first raise [tex]-0.2b^{6}[/tex] to the third power and then multiply the result by 5b. This will give the answer [tex]-0.04b^{19}[/tex], which can be obtained following the below mentioned steps.
Let's do this step by step:
Raise [tex]-0.2b^{6}[/tex] to the third power: [tex](-0.2)^3[/tex]= −0.008 and [tex](b^{6})^3[/tex]= [tex]b^{18}[/tex]
Multiply the result by 5b: [tex](-0.008)b^{18}*5b[/tex] = [tex](-0.008*5)b^{18+1}[/tex] = [tex]-0.04b^{19}[/tex]
The final simplified expression is [tex]-0.04b^{19}[/tex].
Will the standard form 3.2 × 10–4 be more or less than 1? Explain what effect the negative exponent has. Thanks! =)
Richard borrowed $1,250 for two years at 14% a year under an add-on plan. He repaid the loan, including interest, in 24 equal payments. How much was each payment?
Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.
The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.
Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?
Select each correct answer.
(11, 14)
(10, 12)
(12, 10.5)
(15, 11)
(11, 9)
Let
x-------> represents the poodle’s body length
y-------> represents the shoulder height
Constraints
[tex]10\ in \leq y \leq 15\ in[/tex] --------> constraint A
[tex]x \leq 16\ in[/tex] --------> constraint B
[tex]y \leq x+1[/tex] --------> constraint C
Using a graphing tool
see the attached figure
The solution is the shaded area
we know that
If a pair ordered is a solution for a successful poodle measurement
then
the pair ordered meet all the constraints
Let's check each case to determine the solution to the problem
Replace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solution
Case A) [tex](11,14)[/tex]
constraint A
[tex]10\ in \leq 14 \leq 15\ in[/tex] ------> is true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]14 \leq 11+1[/tex]
[tex]14 \leq 12[/tex] -------> is not true
therefore
the pair [tex](11,14)[/tex] does not meet all constraints
Case B) [tex](10,12)[/tex]
constraint A
[tex]10\ in \leq 12 \leq 15\ in[/tex] ------> is true
constraint B
[tex]10 \leq 16\ in[/tex] --------> is true
constraint C
[tex]12 \leq 10+1[/tex]
[tex]12 \leq 11[/tex] -------> is not true
therefore
the pair [tex](10,12)[/tex] does not meet all constraints
Case C) [tex](12,10.5)[/tex]
constraint A
[tex]10\ in \leq 10.5 \leq 15\ in[/tex] ------> is true
constraint B
[tex]12 \leq 16\ in[/tex] --------> is true
constraint C
[tex]10.5 \leq 12+1[/tex]
[tex]10.5 \leq 13[/tex] -------> is true
therefore
the pair [tex](12,10.5)[/tex] meets all constraints
Case D) [tex](15,11)[/tex]
constraint A
[tex]10\ in \leq 11 \leq 15\ in[/tex] ------> is true
constraint B
[tex]15 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](15,11)[/tex] meets all constraints
Case E) [tex](11,9)[/tex]
constraint A
[tex]10\ in \leq 9 \leq 15\ in[/tex] ------> is not true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](11,9)[/tex] does not meet all constraints
therefore
the answer is
[tex](12,10.5)[/tex]
[tex](15,11)[/tex]
in the greenhouse holds 467 plants how many plants can 6 shelves hold
Let f(x)=12x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)?
Answer:
The new function is [tex]g(x)=48x^2+16[/tex]
Step-by-step explanation:
We are given,
The function [tex]f(x)=12x^2+4[/tex] is vertically stretched by a factor of 4.
Now, we know that,
Vertical stretch changes the function f(x) to [tex]kf(x)[/tex] where k is the scale factor.
So, we get,
The new function is [tex]g(x)=4f(x)[/tex]
i.e. [tex]g(x)=4(12x^2+4)[/tex]
i.e. [tex]g(x)=48x^2+16[/tex]
Thus, the equation of the new function is [tex]g(x)=48x^2+16[/tex].
Consider that lines u and v are parallel. Which equation models the relationship between the angles? What is the value of x? A) 12x - 4 = 10x + 10; x = 7 B) 12x - 4 + 10x + 10 = 180; x = 7.9 C) 12x - 4 = 10x - 10; x = -3 D) 12x + 4 = 10x + 10; x = 3
Answer:
A) 12x - 4 = 10x + 10; x = 7
Step-by-step explanation:
12x - 4 = 10x + 10; x = 7
Since lines u and v are parallel, the two angles are corresponding angles. Corresponding angles are equal to each other.
12x - 4 = 10x + 10
Solve for x:
2x = 14
x = 7
sosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Answer:
0
Step-by-step explanation:
the other person is correct! :D
will mark brainliest!!
Find the solution of this system of equations
-3x-7y=-66
-10x-7y=-24
Charlie, who is 4 feet tall, walks away from a streetlight that is 15 feet high at a rate of 6 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time. (Hint: First use similar triangles to express s as a function of the distance d from the streetlight to Charlie.)
fInd the missing term in the following geometric sequence. 4, __, 500
Answer: The missing term in the given geometric sequence is 20√5 or -20√5.
Step-by-step explanation: We are given to find the missing term in the following geometric sequence :
4, ?, 500, . . .
Let b represents the missing term.
Since the given sequence is a geometric one, so there common ratio r such that
[tex]\dfrac{b}{4}=\dfrac{500}{b}=r\\\\\\\Rightarrow \dfrac{b}{4}=\dfrac{500}{b}\\\\\Rightarrow b^2=4\times500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm\sqrt{2000}\\\\\Rightarrow b=\pm20\sqrt{5}.[/tex]
Thus, the missing term in the given geometric sequence is 20√5 or -20√5.
Eben rolls two standard number cubes 36 times. Predict how many times he will roll a sum of 4.
The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: calculate the probability mass function of final temperature
write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
Explanation:To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
The graph shows a line and two similar triangles.
Answer:
Option (a) is correct.
The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]
Step-by-step explanation:
Given : The graph shows a line and two similar triangles.
We have to find the expression that finds the equation of line.
Since, given two triangles are similar.
So, Δ ABC ≅ Δ ADE
Thus, There corresponding sides are in same proportion.
[tex]\frac{AC}{AD}=\frac{CB}{DE}= \frac{AB}{BE}[/tex]
Substitute, we get,
[tex]\frac{1}{y}=\frac{4}{x}= \frac{AB}{BE}[/tex]
Rearrange, we have,
[tex]\frac{1}{4}=\frac{y}{x}= \frac{AB}{BE}[/tex]
Also, finding slope of line AE,
Coordinate of B is (4,1) and Coordinate of A is (0,0)
Th equation of line is y = mx + c
Where, m is slope and c is x intercept
Since, [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{1-0}{4-0}[/tex]
Simplify, we have,
[tex]m=\frac{1}{4}[/tex]
And c = 0
Thus, equation of line is[tex]y=\frac{1}{4}x[/tex]
We re-writing we get,
[tex]\frac{y}{x}=\frac{1}{4}[/tex]
Thus, The equation of the line is expressed using expression [tex]\frac{y}{x}=\frac{1}{4}[/tex]
What is the slope of the line passing through the points (−1, 7) and (4, −1)?
2nd picture is the choices I have.
Jamie had 5 1/4 cans if soup in her kitchen. She decided to use 3 1/9 of it. How much soup does she still have after making 3 1/9 if it?
please explain
A 21-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than six times the length of the first piece. Find the lengths of the pieces
Match the equation with the step needed to solve it.
1 .
subtract m
2m - 1 = 3m
2 .
add 2
2m = 1 + m
3 .
subtract 2m
m - 1 = 2
4 .
add 1
2 + m = 3
5 .
subtract 2
-2 + m = 1
6 .
subtract 1
3 = 1 + m
Answer:
1.
add 1
m - 1 = 2
2.
subtract 1
3 = 1 + m
3.
add 2
-2 + m = 1
4 .
subtract m
2m = 1 + m
5 .
subtract 2
2 + m = 3
6 .
subtract 2m
2m - 1 = 3m
Two trucks were driven on a 1,680 kilometer (km) trip. the first truck averaged 14 km per liter of fuel for the trip, and the second averaged 12 km per liter. the second truck used how many more liters of gas than the first?
The second truck used 20 liters more gas than the first truck.
It is given that two trucks were driven. First truck averages 14 km per liter of fuel whereas the 2nd truck averages 12 km per liter of fuel.
We have to find that how many more liters of gas the 2nd truck used in comparison to 1st truck.
What will be the value if we subtract 20 from 40 ?
The value will be 20.
Fuel used by the first truck will be ;
1680 / 14 = 120 liters
Fuel used by second truck will be ;
1680 / 12 = 140 liters
Difference of fuel used by 1st truck and 2nd truck is
140 - 120 = 20 liters
Thus the second truck used 20 liters more fuel than the first.
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which equation best represents the model?
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive?
Find the constant of variation k for the direct variation
A) k=2.5
B) k=-2
C) k=2
D) k=0.5
Approximately 105 out of 350 teens have their own savings account. Express the ratio 105:350 as a fraction in simplest form.
Nail Polish. A Specific shade of red nail polish requires 7 parts red to 2 parts yellow. A mixture contains 45 quarts. How many quarts of red? How many quarts of yellow?
By setting up a proportion using the given ratio of 7 parts red to 2 parts yellow, we can determine that in a 45-quart mixture, there will be 35 quarts red and 10 quarts yellow.
Explanation:To find out the number of quarts for each color in the mixture, we need to set up a proportion. The given ratio of red to yellow is 7:2. So, for every 9 parts (7 red + 2 yellow), we have a specified amount of nail polish.
The total amount of nail polish we have is 45 quarts. Each 'part' of our ratio can then be calculated as 45 (total quarts) divided by 9 (total parts), which equals 5 quarts per part.
So, for the red nail polish, since it's 7 parts, we have 7 parts * 5 quarts/part = 35 quarts. And for the yellow nail polish, as it's 2 parts, we have 2 parts * 5 quarts/part = 10 quarts.
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Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.
square feet
Answer:
22 square foot
Step-by-step explanation:
Consider PQR be a triangle, such that PQ=9 feet, PR=10 feet.
Now, Perimeter of triangle=24
⇒Sum of all the sides=24
⇒PQ+PR+QR=24
⇒9+10+QR=24
⇒QR=5 feet
Also, s=[tex]\frac{a+b+c}{2}=\frac{9+10+5}{2}=12[/tex]
Area of triangle A=[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
=[tex]\sqrt{12(12-9)(12-10)(12-5)}[/tex]
=[tex]\sqrt{12(3)(2)(7)}[/tex]
=[tex]\sqrt{504}[/tex]
=[tex]22.44[/tex]
≈[tex]22sq foot[/tex]
thus, area of triangle=22 square foot.
Greta completed a mile race in 5 minutes . inez ran a mile in which each quarter mile split was 1 min 20 seconds which of the two girls had the fastest time? How much faster?
When a particular machine is functioning properly, 80% of the items produced are non-defective. if three items are examined, what is the probability that one is defective? use the binomial probability function to answer this question?
Answer:
The probability is 38.4%
Step-by-step explanation: Here we have two posibilites for each of the 3 items, it is defective or it is not.
Where the probability that the item is defective is equal to 20% (or 0.2 in decimal form)
Now, if only one is defective, this means that the other two are not, so the probabilites (at random) are 20%, 80% and 80%.
Then the joint probability, equal to the product of those 3 probabilities, is:
p = 0.2*0.8*0.8 = 0.128
But we have 3 posible permutations (in which different options are the deffective one) so the probability is 3 times that number:
P = 3p = 3*0.128 = 0.384
So the probbility, in percentage form, is 38.4%
1. 48 c = __qt
A. 6
B. 8
C. 10
D. 12
2. 96oz__5 lb
A. <
B. >
C. =
3. 6 yd, 1 ft = __ ft
A. 7
B. 12
C. 19
D. 36
4. 6 1/2 lb = __oz?
A. 104
B. 108
C. 112
D. 136
The units after conversion are:
48 c = 12 qt
96 oz > 5 lb
6 yd, 1 ft = 19 ft
6 1/2 lb = 104 oz
We have,
1.
To convert 48 cups to quarts, we know that there are 4 cups in 1 quart. Therefore, dividing 48 by 4 gives us the number of quarts.
48 cups / 4 cups/quart = 12 quarts
2.
To compare 96 ounces to 5 pounds, we need to convert one of the units so that they are in the same unit of measurement.
Since there are 16 ounces in 1 pound, we can convert 5 pounds to ounces.
5 pounds x 16 ounces/pound = 80 ounces
3.
Now we can compare 96 ounces and 80 ounces.
Since 96 is greater than 80.
4.
To convert 6 yards and 1 foot to feet, we know that there are 3 feet in 1 yard.
Therefore, we can convert the yards to feet and add the 1 foot.
6 yards x 3 feet/yard = 18 feet
18 feet + 1 foot = 19 feet
5.
To convert 6 1/2 pounds to ounces, we know that there are 16 ounces in 1 pound. We can convert the whole number part and the fraction part separately and then add them together.
6 pounds x 16 ounces/pound
= 96 ounces
Now let's convert the fraction:
1/2 pound x 16 ounces/pound = 8 ounces
Adding the two parts together:
96 ounces + 8 ounces = 104 ounces
Thus,
The units after conversion are:
48 c = 12 qt
96 oz > 5 lb
6 yd, 1 ft = 19 ft
6 1/2 lb = 104 oz
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I need help with this problem ASAP. Please.
y=x+√x+5 y=7
Answer:
Solve for
x = 1
y = 7
Step-by-step explanation: