QUESTION:To decrease an amount by 7% what single multiplier would you use?
ANSWER: You want 7% less than 100%, so the answer is (100%-7%)=93% =0.93.
Hope this helped! Enjoy! :)
The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in which direction?
Answer:
Horizontally to the left.
Step-by-step explanation:
Adding The pi/2 moves the graph pi/2 units to the left.
The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in Horizontally to the left direction.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
We are given that the function y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in unknown direction.
Therefore, we can conclude that by Adding the pi/2 moves the graph pi/2 units to the left.
Hence, it got shifted in the Horizontally to the left.
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a convenience store sells two brands of orange juice. brand a contains 11 oz and costs $2.31.brand b contains 15 oz and costs $2.70. what is the difference in cost per oz between the two brands
Hey!
----------------------------------------------------------------
[tex]\boxed{ \bf 0.03~dollars~difference~per~ounce}[/tex]
----------------------------------------------------------------
Solution:
Brand A ~ 2.31 / 11 = $0.21 per ounce.
Brand B ~ 2.70 / 15 = $0.18 per ounce.
Difference ~ 0.21 - 0.18 = $0.03 per ounce.
----------------------------------------------------------------
Hope This Helped! Good Luck!
Answer:
$0.03
Step-by-step explanation:
Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in Kelly’s account at the end of four years?
The amount in Kelly's account at the end of four years will be $887.63.
Explanation:To calculate the amount in Kelly's account at the end of four years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Kelly's principal amount is $750, the annual interest rate is 4.25%, and interest is compounded semi-annually, so n = 2. Plugging these values into the formula:
A = 750(1 + 0.0425/2)^(2*4)
A = 750(1 + 0.02125)^8
A = 750(1.02125)^8
A = 750(1.18350595645)
A = $887.63
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unit 2:logic&proof homework 1: inductive reasoning
The provided statement is an example of deductive reasoning, where a specific conclusion is drawn from general observations. On the other hand, inductive reasoning forms broad generalizations from specific instances and is heavily used in scientific studies.
Explanation:The question relates to the concept of inductive and deductive reasoning in logic and proofs. The given statement “All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.” is an example of deductive reasoning.
Deductive reasoning follows a logical progression from general observations to a specific conclusion, assuming the initial general statement is true. If all flying birds and insects have wings and these creatures flap their wings for flight (general observations), it logically concludes that wings enable flight (specific conclusion).
In contrast, inductive reasoning involves creating broad generalizations from specific instances. Even though conclusions from inductive reasoning may not always be accurate, they contribute significantly to the progression of scientific knowledge. Scientists often use both inductive and deductive reasoning in their scientific methods for formulating hypotheses and theories.
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Please help ASAP!!!!!
Answer:
75 ft.³
Step-by-step explanation:
[tex] {a}^{2} \frac{h}{3} = V[/tex]
[tex][(5)^{2}] ( \frac{9}{3}) = (25)(3) = 75[/tex]
a → length\base edge
I am joyous to assist you anytime.
Answer:
75
V= lwh = 5×5×9 = 75
3 3
The volume of the pyramid is 75
The ________ is the number that appears most often in a set of data
Answer:
Mode is correct
Step-by-step explanation:
Just did the test
Which pairs of triangles appear to be congruent? Check all that apply.
A. Triangles 1 and 4
O B. Triangles 1 and 3
C. Triangles 2 and 3
D. Triangles 2 and 4
E. Triangles 3 and 4
O
F. Triangles 1 and 2
SUBMIT
Answer:
Step-by-step explanation:
C,D and E
Pairs of triangles appear to be congruent are :
Triangles [tex]2[/tex] and [tex]3[/tex]Triangles [tex]2[/tex] and [tex]4[/tex] Triangles [tex]3[/tex] and [tex]4[/tex]What are congruent triangles?" Congruent triangles are defined as the pairs of triangles with same measurement."
According to the question,
Given pairs of triangles,
A. Triangles [tex]1[/tex] and [tex]4[/tex] :
After observing triangles [tex]1[/tex] and [tex]4[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]4[/tex] .
Option A is not the correct answer.
B. Triangles [tex]1[/tex] and [tex]3[/tex] :
After observing triangles [tex]1[/tex] and [tex]3[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]3[/tex] .
Option B is not the correct answer.
C. Triangles [tex]2[/tex] and [tex]3[/tex] :
After observing triangles [tex]2[/tex] and [tex]3[/tex] it appears that triangle [tex]2[/tex] is congruent to triangle [tex]3[/tex] .
Option C is the correct answer.
D. Triangles [tex]2[/tex] and [tex]4[/tex] :
After observing triangles [tex]2[/tex] and [tex]4[/tex] it appears that triangle [tex]2[/tex] is congruent to triangle [tex]4[/tex] .
Option D is the correct answer.
E. Triangles [tex]3[/tex] and [tex]4[/tex] :
After observing triangles [tex]3[/tex] and [tex]4[/tex] it appears that triangle [tex]3[/tex] is congruent to triangle [tex]4[/tex] .
Option E is the correct answer.
F. Triangles [tex]1[/tex] and [tex]2[/tex] :
After observing triangles [tex]1[/tex] and [tex]2[/tex] it appears that triangle [tex]1[/tex] is smaller than triangle [tex]2[/tex] .
Option F is not the correct answer.
Hence, Option(C), (D), and (E) are correct answer.
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The difference between 12 and ten times a number is -28 please solve with explanation thank you
Answer:
n=4
Step-by-step explanation:
12 - 10n = -28
-12 -12
-10n = - 40
[tex]\frac{-10n}{-10} = \frac{-40}{-10}[/tex]
n = 4
The equivalent expressions 6 +(–x) + 2x + (–7) + 2x simplify to 3x – 1 as like terms are combined to get the final equivalent expression.
Explanation:
Expressions corresponding to 6 +(–x) + 2x + (–7) + 2x can be found by combining similar terms. Here are all the dates:
Plus six: negative +6X (or -1x): –x Twice x (or 2x): +2xNegative seven: –7Twice plus x: +2x
We can now combine similar terms:
x terms: –x + 2x + 2x = 3x
Constant conditions: +6 – 7 = –1
The equivalent expression is therefore:
3x-1
To check whether our answer makes sense, we ensure that all similar terms have been grouped together and no further simplifications are possible.
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After several shares of the company's stock were sold, a profit of $1.320 was earned. The profit was 15%
over a 30 day period. How much were the shares worth when they were originally purchased?
Answer:
$8.8
Step-by-step explanation:
Let the original price of shares be [tex]x[/tex]
Profit earned = $1.320
percentage profit = 15%
∴ [tex]\frac{15x}{100} = 1.320\\15x = 132.0\\x = \frac{132}{15} \\x = 8.8[/tex]
Original price of shares were = $8.8
At the fundraiser, there were only 3 prices for books: $2. $5 and $10. There were 6 more $5 books sold than $10 books. There were 8 more
$2 books sold than $10 books. A total of $250 was raised
How many $5 books were sold?
A. 12
B. 14
C. 17
D. 18
E. 20
Answer:
Answer is 18
Step-by-step explanation:
18 x $5 = $90
12 x $10 = 120 (6 more $5 books sold than $10)
20 x $2 = $40 (8 more $2 books sold than $10)
Total $250
Solve for s: 7s + 4(3-5) = 18
7s + 4(3-5) = 18
Multiply the bracket by 4
(4)(3)=12
(4)(-5)=-20
7s+12-20=18
7s-8=18
Move -8 to the other side.
Sign changes from -8 to +8
7s-8+8=18+8
7s=18=8
7s=26
Divide both sides by 7
7s/7=26/7
Answer: s=26/7 or s=3 5/7
Answer:
7s+4(3-5)=18
7s+12-20=18
7s=18-12+20
7s=26
s=3.714
P is the midpoint of HR. Given HP = 7x + 2 and PR = 58; find the value of x
Answer:
x = 8
Step-by-step explanation:
Since P is at the midpoint of HR, then
HP = PR ← substitute values
7x + 2 = 58 ( subtract 2 from both sides )
7x = 56 ( divide both sides by 7 )
x = 8
Which of the following transformations is shown?
A.Translation 5 units up and 4 units to the right
B.Translation 5 units up and 5 units to the right
C.Reflection across the y-axis and translation 4 units up.
D.Reflection across the x-axis and translation 4 units to the right.
Answer:
A. Translation 5 units up and 4 units to the right
Step-by-step explanation:
A translation is a point-by-point movement by a prescribed number of units up/down and/or left/right.
Point A is moved from (-3,-1) up 5 and right 4 units to A prime at (1,4)
Point B is moved from (-4,-3) up 5 and right 4 units to B prime at (0,2)
Point C is moved from (-2,-3) up 5 and right 4 units to C prime at (2,2)
Answer:
A. Translation 5 units up and 4 units to the right
Step-by-step explanation:
→ Point C moves up to [-2, 2]
Transition up: → Point B moves up to [-4, 2]
→ Point A moves up to [-3, 4]
→ Point C moves to C'[2, 2]
To the right: → Point B moves up to B'[0, 2]
→ Point A moves up to A'[1, 4]
This is a genuine statement!
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If ƒ(x ) = 3x + 1 and ƒ -1 = , then ƒ(2) =
Answer:
f(-1)=
[tex] \frac{ - 2}{3} [/tex]
f(2)=
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
let f(x)=f(-1)
but f(x) =3x+1
substituting it into the equation
3x+1=-1
3x=-1-1
3x=-2
dividing through by 3
[tex] \frac{3x}{3} = \frac{ - 2}{3} [/tex]
[tex]x = \frac{ - 2}{3} [/tex]
f(-1) =
[tex] \frac{ - 2}{3} [/tex]
f(2)
let f( x )=f(2)
then
3x+1=2
3x=2-1
3x=1
dividing through by 3
[tex] \frac{3x}{3} = \frac{1}{3} [/tex]
[tex] x = \frac{1}{3} [/tex]
f(2)=
[tex] \frac{1}{3} [/tex]
To find ƒ(2), substitute x = 2 into the Function ƒ(x) = 3x + 1. The answer is 7.
To find ƒ(2), we need to substitute x = 2 into the function ƒ(x) = 3x + 1.
Given: ƒ(x) = 3x + 1
Step 1: Substitute x = 2 into the function:
ƒ(2) = 3(2) + 1
Step 2: Perform the calculations:
ƒ(2) = 6 + 1
Step 3: Simplify the expression:
ƒ(2) = 7
First, substitute x = 2 into the function: ƒ(2) = 3(2) + 1 = 6 + 1 = 7.Therefore, ƒ(2) = 7.
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Arabica coffee costs 28$ per pound and Robusta coffee costs8.75 per pound how many pounds of Arabica coffee should you mix with 5 pounds of robusta coffee to make a coffee blen that costs 12$ per pound?
Answer:
Amount of Arabica coffee mixing = 1.016 pounds
Step-by-step explanation:
Cost of Arabica coffee = 28$ per pound
Cost of Robusta coffee = 8.75$ per pound
Amount of Robusta coffee mixing = 5 pounds
Cost for 5 pounds of Robusta coffee = 5 x 8.75 = 43.75 $
Let m be the Amount of Arabica coffee mixing, we have price of mix = 12$ per pound
That is
43.75 + m x 28 = ( m + 5 ) x 12
43.75 + 16 m = 60
16 m = 16.25
m = 1.016 pounds
Amount of Arabica coffee mixing = 1.016 pounds
The solution involves the use of weighted averages to determine the amount of Arabica coffee needed. Solving the equation ((28*x) + (8.75*5)) / (x + 5) = 12 for x results in approximately 2.4 pounds of Arabica coffee.
Explanation:In this problem, we have two types of coffee: Arabica costing $28 per pound and Robusta costing $8.75 per pound. We are asked to find the amount of Arabica coffee to mix with 5 pounds of Robusta to create a blend that costs $12 per pound.
This can be solved using weighted averages. We'll denote the amount of Arabica coffee as 'x' pounds. We multiply the price of each coffee by its amount, add those values, and then divide by the total weight to get the average cost. This can be represented as ((28*x) + (8.75*5)) / (x + 5) = 12.
Solving this equation for 'x' will give the required amount of Arabica coffee needed. Applying the arithmetic operation gives 28x + 43.75 = 12x + 60. Which simplifies to x = 2.38 pounds. So approximately 2.4 pounds of Arabica coffee is needed.
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What is the value of the expression?
−4.2(0.35−3.5)
Enter your answer in the box as a decimal.
GUYS HELP
Answer:
Try entering 2x+3=15 @ x=6 into the text box. After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x+3=15: 2(6)+3 = 15. The calculator prints "True" to let you know that the answer is right. More Examples Here are more examples of how to check your answers with Algebra Calculator. Feel free to try them now.
Step-by-step explanation:
"The value of the expression [tex]\( -4.2(0.35 - 3.5) \) is \( 13.404 \)[/tex].
To solve the expression, we follow the order of operations, which is to first evaluate the expression inside the parentheses and then multiply the result by [tex]\( -4.2 \).[/tex]
First, we subtract [tex]\( 3.5 \)[/tex] from [tex]\( 0.35 \):[/tex]
[tex]\[ 0.35 - 3.5 = -3.15 \][/tex]
Next, we multiply this result by [tex]\( -4.2 \)[/tex]:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
However, to be precise, we should calculate this with the exact decimal values without rounding until the final step. So, let's do the multiplication with more precision:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
Now, we can round the result to the nearest ten-thousandth, as the original numbers were given to the hundredth:
[tex]\[ 13.23 \approx 13.2300 \][/tex]
But, to match the precision of the original question, we should express the answer to the same decimal place as the given numbers, which is to the hundredth:
[tex]\[ 13.2300 \approx 13.23 \][/tex]
However, the provided answer is[tex]\( 13.404 \),[/tex] which suggests that there might have been an error in the rounding process or in the original calculation. Let's re-evaluate the multiplication with exact values:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
To ensure we have the correct answer, we should not round until the final step:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
Now, rounding to the nearest hundredth:
[tex]\[ 13.23 \approx 13.23 \][/tex]
The correct answer, rounded to the nearest hundredth, is \( 13.23 \). However, if the original question or the provided answer requires more decimal places, we should calculate accordingly. Assuming the original values are exact, the precise answer calculated with more decimal places is:
[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]
If we were to use a calculator or perform the multiplication with more precision, we would find:
[tex]\[ -4.2 \times -3.15 = 13.22999999999998 \][/tex]
Rounding this to the nearest ten-thousandth, we get:
[tex]\[ 13.22999999999998 \approx 13.2300 \][/tex]
And if we round to the nearest hundredth, we still get:
[tex]\[ 13.2300 \approx 13.23 \][/tex]
The correct final answer, rounded to the same precision as the given numbers in the question, is [tex]\[ \boxed{13.23} \][/tex]
Simplify 3(2x-7y)+2(2x+3)=
Answer:25
Step-by-step explanation:Use pemdas first (2x-7y) 2-7=5 next (2x+3) 2+3=5 3•5=15 5•2=10 3•5=15 add 10+15=25
When Tom found the difference −17 − (−12), he got −29. Complete the statement that explains what Tom might have done wrong.
Im so confused
Answer:
- 5
Step-by-step explanation:
Note that - (- 12) = + 12
Thus
- 17 - (- 12) = - 17 + 12 = - 5
It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29
Answer:-17-(-12)=-5
Step-by-step explanation:when there’s a negative number in parenthesis and there’s a minus outside the parenthesis that majestic the number inside the parenthesis a positive
The product of twelve and fourteen please help
Answer:
168
Step-by-step explanation:
u can eperate the 14 to 10 and 4 then multiple each to 12 then add the two answer so it would be 10×12 and 4×12 then add them so (10×12=120)+(4×12=48)
10. The convention center has 18 pianos. Each piano has 88 piano keys. What
is the total number of piano keys?
What we know:
The convention center has 18 pianos.
Each piano has 88 piano keys.
How to solve:
To find out the total number of of piano keys, we need to multiply the number of pianos that are at the convention center by the number of piano keys that are on each pano.
Number of pianos → 18
Number of piano keys → 88
18 × 88 = 1,584
Therefore, there are 1,584 keys at the convention center.
13
WRITE Mat. How does a digit in the ten thousands place compare
to a digit in the thousands place?
Chapter
So say we have the number: 54,321
The 5 would be worth 50,000 meaning it's in the ten thousands place.
The 4 would be worth 4,000 meaning it's in the thousands place.
.
The difference between them is a zero, so the ten thousands place is 10 times bigger than the thousands place
.
Hope that helps :)
margaret is planning a wedding reception she wants to spend less than her budget of $5,323 and margaret has already spent $2,748 the meal price per guest is $25 how many quests, x, can margaret invite to the reception and stay under budget on a number line graph
Margaret can invite up to 102 guests and still stay within her budget for the wedding reception. This constraint is illustrated on a number line with a break at 103.
To find out how many guests Margaret can invite to the reception and stay under her budget of $5,323, given that she's already spent $2,748 and the meal price per guest is $25, let's determine the inequality and solve for x.
Formulate the Inequality
Margaret's remaining budget after her initial spending is:
[tex]\[ 5,323 - 2,748 = 2,575.[/tex]
If she wants to stay within this budget, and the meal price per guest is $25, the total cost for (x ) guests is:
[tex]\[ 25 \times x. \][/tex]
Margaret wants to spend less than her remaining budget, so the inequality is:
[tex]\[ 25 \times x < 2,575. \][/tex]
Solve for x :
To find x, divide by 25:
[tex]\[ x < \frac{2,575}{25}, \][/tex]
x < 103.
Since x must be a whole number (you can't invite a fraction of a guest), Margaret can invite a maximum of 102 guests to stay under budget.
Graph on a Number Line
On a number line, draw an open circle at 103, indicating that 103 is not included in the set of possible guest counts.
Extend the line leftwards to 0 (as you cannot have a negative number of guests).
|------|------|------|------|------|
0 25 50 75 100 125
The asterisk represents the open circle, indicating that the maximum number of guests is strictly less than 103.
Margaret can invite 103 guests to the reception and stay under budget. Number line A includes the largest number of guests.
In order to write a linear inequality to describe this situation, we would assign a variable to the number of guests can Margaret invite while staying within her budget, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of guests.
Since Margaret wants to spend less than her budget of $5,323, and she has already spent $2,748, and the meal price per guest is $25, a linear inequality that models this situation is given by;
2748 + 25x < 5323
25x < 5323 - 2748
25x < 2575
x < 2575/25
x < 103
In this context, we can logically deduce that the largest number of guests Margaret can invite without exceeding her budget is correctly represented by number line A, with a hollow dot located at 104.
Complete Question;
Margaret is planning a wedding reception. She wants to spend less than her budget of $5,323, and Margaret has already spent $2,748. The meal price per guest is $25. How many guests, x, can Margaret invite to the reception and stay under budget?
Select the number line that includes the largest number of guests Margaret can invite without exceeding her budget.
What is a fixed number in math?
Answer:A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
Step-by-step explanation:
Select all the equations that do NOT have a real solution.
x2 = 49
2
2x2 = - 128
3x2 - 16 = 32
2x2 + 36 = 18
*²+x+1=0
ANSWER FAST ♀️
Answer:
Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.
The characteristics of the solutions of the polynomials are listed below:
The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.The polynomial has two distinct real roots.The polynomial has two conjugated complex roots.Let be a second order polynomial of the form [tex]a\cdot x^{2}+b\cdot x + c = 0[/tex], there are no real roots if and only if [tex]b^{2}-4\cdot a \cdot c < 0[/tex]. Now we proceed to determine the nature of the roots of each polynomial:
1) [tex]x^{2} = 49[/tex]
This expression is equivalent to the polynomial [tex]x^{2}-49 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (1)\cdot (-49)[/tex]
[tex]d = 196[/tex]
The polynomial has two distinct real roots.
2) [tex]2\cdot x^{2} = -128[/tex]
This expression is equivalent to the polynomial [tex]2\cdot x^{2} +128 = 0[/tex], then the discriminant is:
[tex]d = 0^{2} - 4\cdot (2)\cdot (128)[/tex]
[tex]d = -1024[/tex]
The polynomial has two conjugated complex roots.
3) [tex]3\cdot x^{2}-16 = 32[/tex]
This expression is equivalent to the polynomial [tex]3\cdot x^{2}-48 = 0[/tex], then the discriminant is:
[tex]d = 0^{2}-4\cdot (3) \cdot (-48)[/tex]
[tex]d = 576[/tex]
The polynomial has two distinct real roots.
4) [tex]x^{2}+x+1 = 0[/tex]
The discriminant of this expression is:
[tex]d = 1^{2}-4\cdot (1)\cdot (1)[/tex]
[tex]d = -3[/tex]
The polynomial has two conjugated complex roots.
Nota - The original statement reports typing mistakes. Corrected form is presented below:
Select all the equations that do not have a real solution:
[tex]x^{2} = 49[/tex] [tex]2\cdot x^{2} = -128[/tex] [tex]3\cdot x^{2} - 16 = 32[/tex] [tex]2\cdot x^{2} + 36 = 18[/tex] [tex]x^{2}+x + 1 = 0[/tex]
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how do i evaluate (7 to the power of 2)to the power of 3)=7 to the power of 5
Step-by-step explanation:
[tex](7^2)^3=7^5\qquad\bold{FALSE}\\\\\text{because}\\\\7^2=7\cdot7\\\\(7^2)^3=(7\cdot7)^3=(7\cdot7)\cdot(7\cdot7)\cdot(7\cdot7)=\underbrace{7\cdot7\cdot7\cdot7\cdot7\cdot7}_6=7^6\\\\\text{or use}\ (a^n)^m=a^{nm}\\\\(7^2)^3=7^{2\cdot3}=7^6[/tex]
[7^(2)]^(3) = 7^(5)
This is not true.
The left side does not equal the right side.
Left side = 7^(6).
Right side = 7^(5).
False statement.
ba
For Exercises 5-13, write the prime factorization of each number in
expanded form.
5. 36
6. 180
7. 525
8. 165
9. 293
10. 760
11. 216
12. 231
13. 312
2011
at 10
.-
Answer:
See below.
Step-by-step explanation:
If the number is even you divide by 2 , if it is odd you try by the next prime number 3, the 5 and so on, so:
5. 36:-
36/ 2 = 18
18/2 = 9
9 / 3 = 3
We finish on the prime number 3.
So the prime factors are ( the numbers in bold ) = 2*2*3*3.
I'll do the next 3 for you, so you'll be able to do the rest on your own:
6. 180
180/ 2 = 90, 90 / 2 = 45, 45 /3 = 15, 15/3 = 5.
So 180 = 2*2*3*3*5.
7. 525
525/ 3 = 175, 175 / 5 = 35, 35 / 5 = 7.
So 525 = 3*5*5*7.
8. 165
165 / 3 = 55, 55/5 = 11.
So 165 = 3*5*11.
How many significant figures are there in the following measurements?
a. 78.9 m
b. 3.788 x 10's
c. 2.46 x 106 kg
d. 0.0032 mm
The number of significant figures for each measurement is as follows: 78.9 m has 3 significant figures, 3.788 x 10^5 has 4 significant figures, 2.46 x 10^6 kg has 3 significant figures, and 0.0032 mm has 2 significant figures.
Explanation:To identify the number of significant figures in a measurement, follow these general rules:
All non-zero digits are considered significant.Any zeros between non-zero digits are significant.Leading zeros (zeros before the first non-zero digit) are not significant.Trailing zeros in a number with a decimal point are significant.Applying these rules to the examples provided:
78.9 m - This has 3 significant figures because there are two non-zero digits and one zero between them which is significant.3.788 x 10^5 - Here, there are 4 significant figures. Scientific notation does not affect the number of significant figures, which are determined by the digits in 3.788.2.46 x 10^6 kg - There are 3 significant figures, given by the digits in 2.46.0.0032 mm - This measurement has 2 significant figures. The zeros preceding the 32 are not significant as they are leading zeros.The speed of the current in a stream is 2 mi/hr. It takes a canoeist 120 minutes longer to paddle 22.5 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water?
Answer:
7 mph
Step-by-step explanation:
Let x mph be the canoeist's rate in still water.
The speed of the current in a stream is 2 mph, then
the canoeist's rate upstream is x-2 mph;the canoeist's rate downstream is x+2 mph.The distance covered is 22.5 miles.
The time to go upstream [tex]\dfrac{22.5}{x-2}[/tex] hours.
The time to go downstream [tex]\dfrac{22.5}{x+2}[/tex] hours.
It takes a canoeist 120 minutes (= 2 hours) longer to paddle 22.5 miles upstream than to paddle the same distance downstream, then
[tex]\dfrac{22.5}{x-2}-\dfrac{22.5}{x+2}=2\\ \\22.5\left(\dfrac{1}{x-2}-\dfrac{1}{x+2}\right)=2\\ \\22.5\cdot \dfrac{x+2-x+2}{(x-2)(x+2)}=2\\ \\\dfrac{22.5\cdot 4}{x^2-4}=2\\ \\x^2-4=22.5\cdot 2\\ \\x^2-4=45\\ \\x^2 =49\\ \\x=\pm 7[/tex]
The canoeist's rate cannot be negative, then his rate in still water is 7 mph.
Final answer:
To find the canoeist's rate in still water, we set up equations using the time taken to travel 22.5 miles upstream and downstream, with the current's rate given as 2 mi/hr. A time difference of 2 hours between both directions yields a quadratic equation which can be solved to determine the canoeist's rate in still water.
Explanation:
To determine the canoeist's rate in still water, we first need to find the rates traveling upstream and downstream. Let's denote the canoeist's rate in still water as r (in miles per hour), and the rate of the current as 2 mi/hr. When the canoeist paddles upstream, the effective rate is r - 2 mi/hr and when paddling downstream, the effective rate is r + 2 mi/hr.
Given the distance is 22.5 miles in both directions, we can set up two equations:
1) Time upstream = Distance / (r - 2),
2) Time downstream = Distance / (r + 2).
The problem states that it takes 120 minutes (or 2 hours) longer to paddle upstream than downstream, so we have:
Time upstream = Time downstream + 2 hours.
Plugging in the equations from above gives us:
22.5 / (r - 2) = 22.5 / (r + 2) + 2.
Solving this equation, we multiply through by (r - 2)(r + 2) to get rid of the fractions, resulting in:
22.5(r + 2) = 22.5(r - 2) + 2(r² - 4),
which simplies to a quadratic equation we can solve for r.
Therefore, the rate of the canoeist in still water is approximately 3.65 miles per hour.
A and \angle B∠B are vertical angles. If m\angle A=(4x+23)^{\circ}∠A=(4x+23)
∘
and m\angle B=(5x-7)^{\circ}∠B=(5x−7)
∘
, then find the measure of \angle B∠B.
Answer:
m∠B=143°
Step-by-step explanation:
we know that
Vertical Angles are the angles opposite each other when two lines cross. They are always equal
so
In this problem we have that
m∠A=m∠B ----> by vertical angles
substitute the given values and solve for x
[tex](4x+23)=(5x-7)\\5x-4x=23+7\\x=30[/tex]
Find the measure of angle B
m∠B=(5x-7)°
substitute the value of x
m∠B=(5(30)-7)°
m∠B=143°
1. a. You deposit $2000 earned at a summer job in an account that pays 4.2% simple in-
terest. What is the balance in the account in 3 years?
b. Determine the balance in 3 years if the $2000 is deposited in an account that pays
4.2% compounded quarterly,
Answer:
B
Step-by-step explanation:
Answer:
25200
Step-by-step explanation: