[tex]0.5x+\dfrac{7}{8}=5\qquad\text{multiply both sides by 8}\\\\4x+7=40\qquad\text{subtract 7 from both sides}\\\\4x=33\qquad\text{divide both sides by 4}\\\\\boxed{x=\dfrac{33}{4}\to x=8\dfrac{1}{4}}[/tex]
Write the expression 2a+b in the form of a fraction with a denominator of: b
[tex]2a+b=\dfrac{2ab}{b}+\dfrac{bb}{b}=\dfrac{2ab}{b}+\dfrac{b^2}{b}=\boxed{\dfrac{2ab+b^2}{b}}[/tex]
Quinn is twice as old as karl and four years older than parker. The sum their ages is 21. How old is Parker
Answer:
Parker is 6 years old
Step-by-step explanation:
Parker is 6 years old
Step-by-step explanation:Let q, p, k represent the ages of Quinn, Parker, and Karl, respectively.
... q = 2k . . . . . . Quinn is twice as old as Karl
... q = p+4 . . . . . Quinn is 4 years older than parker
... q + p + k = 21 . . . . the sum of their ages is 21
_____
We can use the first two equations to find Karl's age in terms of Parker's.
... p+4 = q = 2k
... (p+4)/2 = k
Now, we can substitute for q and k in the last equation.
... (p+4) +p +(p+4)/2 = 21
... 5/2p +6 = 21 . . . . . . collect terms
... p = (2/5)(21 -6) . . . . subtract 6, multiply by 2/5
... p = 6 . . . . . . Parker is 6 years old
How much of the 8% solution should we use to make 100g of a 3% solution?
This is all I have don't ask me any questions I don't know anything else about this
Answer:
37.5 g
Step-by-step explanation:
The final solution will contain 3% × 100 g = 3 g of solute. This amount of solute will be found in w grams of 8% solution, where ...
... 3 = 0.08 × w
... 3/0.08 = w = 37.5 . . . . . grams of 8% solution
Answer:
37.5 grams
Step-by-step explanation:
;)
I forgot how to this can someone help please
Answer:
1728
Step-by-step explanation:
You could write it like this
5.4 * 10^5 * 3.2 * 10^-3
You could do this by multiplying the numbers first
5.4 * 3.2 = 17.28
Now work with the powers of 10
10^5 * 10^-3 = 10^(5 - 3) = 10^2
10^2 = 100
So the answer is 17.28 * 100 = 1728
Ralph wants to purchase a renters insurance policy for his new apartment. His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment. Below is a list of items Ralph made of the items he has in his apartment that he would like to be insured with his policy. What will Ralph’s annual renters insurance premium be? Ralph's Stuff Value TV $150 VCR $60 DVD Player $100 Stereo $80 Sofa $200 Entertainment Center $100 Microwave $40 Coffee Maker $20 Computer $850 Bicycle $200 Coin Collection $600 Pictures/Posters $175 a. $17.88 b. $35.48 c. $214.58 d. $425.65 Please select the best answer from the choices provided A B C D Mark this and return
Answer:
d. $425.65
Step-by-step explanation:
The total value of Ralph's stuff is ...
... 150 + 60 + 100 + 80 + 200 + 100 + 40 + 20 + 850 + 200 + 600 + 175 = 2575
The premium is 16.53% of that, so is ...
... 0.1653 × 2575 = 425.65
Answer:
The insurance company charges an annual premium of $425.65 .
Option (d) is correct .
Step-by-step explanation:
As given
Ralph wants to purchase a renters insurance policy for his new apartment.
His insurance company charges an annual premium of 16.53% of the approximate value of the items he owns and is keeping in his apartment.
Total amount of the items he owns and is keeping in his apartment = TV cost + VCR cost + DVD Player cost + Stereo cost + Sofa cost + Entertainment centre cost + Microwave cost + Coffee Maker cost + Computer cost + Bicycle cost + Coin Collection cost + Pictures/Posters cost
Putting all the values in the above
Total amount of the items he owns and is keeping in his apartment = $150 + $60 +$100 + $ 80 + $200 + $100 + $40 + $20 + $850 + $ 200 + $ 600 + $ 175
Total amount of the items he owns and is keeping in his apartment = $ 2575
16.53 % is written in the decimal form .
[tex]= \frac{16.53}{100}[/tex]
= 0.1653
Insurance company charges an annual premium = 0.1653 × Total amount of the items he owns and is keeping in his apartment .
= 0.1653 × 2575
= $ 425.65 (Approx)
Therefore the insurance company charges an annual premium of $425.65 .
Option (d) is correct .
What isn't the volume of the cylinder below? Radius 8 height 3
Answer: The volume is 603.19, so whichever answer doesn't equal that.
Step-by-step explanation:
V= πr^2h
V= π(8)^2(3)
V= 603.19
Volume = 192πunits³
Work is provided in the image attached.
Eric is 6 1/6 feet tall and his brother is 5 3/4 feet tall. Eric is how many feet taller than his brother?
A. 1/5 feet
B. 5/12 feet
C. 7/12 feet
D. 3/4 feet
Answer:
B. 5/12 feet
Step-by-step explanation:
We know that Eric is [tex]6\frac{1}{6}[/tex] feet tall while his brother is [tex]5\frac{3}{4}[/tex] feet tall. We are supposed to find out how many feet is Eric taller than his brother.
So basically we have to find the difference between the height of the two brothers.
First, let's just change the mixed numbers to improper fractions:
[tex]6\frac{1}{6}[/tex] = [tex]\frac{37}{6}[/tex]
[tex]5\frac{3}{4}[/tex]= [tex]\frac{23}{4}[/tex]
Now taking their difference:
[tex]=\frac{37}{6} -\frac{23}{4}\\\\=\frac{148-138}{24}\\\\=\frac{10}{24}\\\\=\frac{5}{12}[/tex]
Therefore, Eric is 5/12 feet taller than his brother.
Evaluate the expression 3a+2b/2 when a = -3 and =-4
The solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given the expression as :
⇒ 3a + 2b/2
when a = -3 and b = -4
Substitute the values of a and b
⇒ 3 × (-3) + 2 × (-4/2)
⇒ -9 - 4
⇒ -13
Hence, the solution of the expression 3a+2b/2 is -13 when a = -3 and b = -4
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please help i will give brainliest
For this case, we have that by definition:
Let "x" be an angle of any vertex of a right triangle.
[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]
So, if we want to find the tangent of angle A:
[tex]tangent (A) = \frac {6} {8}[/tex]
Thus, the tangent of angle "A" is [tex]\frac {6} {8}[/tex]
Answer:
[tex]\frac {6} {8}[/tex]
Option b
A local garden club had 14 members with a mean age of 34. Then two new members joined. One was 24 years old, and the other was 36 years old. How did the mean age change after they joined? The mean age increased. The mean age decreased. It isn't possible to determine how the mean would change. The mean age stayed the same.
The mean age decreased.
Step-by-step explanation:I find it convenient to look at the additions with respect to the current mean age.
The current total age is 14×34. We have added members with ages (34 -10) and (34 +2), so the new total age is ...
... (34×14) + (34 -10) + (34 +2) = (16×34) - 8
Dividing this total by 16 will give the new mean age. (We already know it is less than 34.)
... ((16×34) -8)/16 = 34 - 1/2 = 33 1/2 . . . new mean age; a decrease
Abby buys 1 sheet of stickers. 5 strips of ten and 9 singles. How many stickers did she buy?
Which of the following is defined by distinct lines which intersect at right angles and at exactly one point
please help me asap!
Answer:
2968.30 cm cube.
Step-by-step explanation:
Given is a cone and top of it is a hemisphere of radius 9 cm.
Cone has height as 17 and radius same 9 cm.
We have to find the volume of the compound shape
We find that the volume would be the sum of that of hemisphere of radius 9 cm and cone of height 17, and radius 9 cm.
Volume of compound shape = volume of cone+Volume of hemisphere
= [tex]\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]
substitute for h and r in the equation
Required volume =
[tex][tex]\frac{1}{3}\pi r^{2} (h+2r) = \frac{1}{3}\pi 9^{2} (17+2(9))\\= 1441.99+1526.31\\=2968.30[/tex][/tex]
So answer is 2968.30 cm cube.
=
Ming is given the following function and asked to find b. f(x)=15(b)x If f(4) = 1215, what is one possible value of b?
Step-by-step explanation:
f(x) = 15(b)x
f(4) = 1215
15(b)4 = 1215
(15)(4)b = 1215
60b = 1215
60b / 60 = 1215 / 60
b = 20.25
Check the answer
15 * 20.25 * 4 = 1215
Answer:
3
Step-by-step explanation:
if you did this on prepworks its 3.
1215=15(b)4
121515=(b)4
81=b4
92=b4
(32)2=b4
34=b4
b = ±3
Can someone please answer this for me.
Answer:
See picture
Step-by-step explanation:
The rule is ...
[tex]x^{m/n}=\sqrt[n]{x^m}[/tex]
The index of the surd becomes the denominator of the exponents inside.
Answer:
x^(5/3)*y^(1/3)
Step-by-step explanation:
note (a*b)^c = a^c*b^c
the given expression can be rewritten as (x^5*y)^1/3
=x^(5/3)*y^(1/3)
ans is the 2nd choice
For what values of x does the following hold true:
a. (5x+3)^2=5(x+3)
b. (3x+10)^2=3(x+10)
c. (3x−8)^2=3x^2−8x
a. x ∈ {-1.2, 0.2}
b. x ∈ {-4 2/3, -1 2/3}
c. x ∈ {2 2/3, 4}
Step-by-step explanation:For this sort of exercise, I find a graphing calculator to be very handy. While the one shown in the attachment (Desmos) can solve the equation as written, I find it convenient to recast the equation to the form f(x) = 0. The calculator finds the values of zero crossings very nicely. Some, like my TI-84, will show the value to 8 or 10 significant digits. Here, 4 digits is sufficient to determine the exact solution.
_____
If you want to work these by hand, you rewrite them to standard form, then use factoring, completing the square, or the quadratic formula to solve them.
a. 25x² +30x +9 -5x -15 = 0 . . . . subtract the right side
... 25x² +25x -6 = 0 . . . . . . . . . . . collect terms
... (5x+6)(5x-1) = 0 . . . . . . . . . . . . . factor (the graphing calc helps here)
... x = -6/5, 1/5
b. 9x² +60x +100 -3x -30 = 0 . . . . subtract the right side
... 9x² +57x +70 = 0 . . . . . . . . . . . . collect terms
... (3x +14)(3x +5) = 0 . . . . . . . . . . . factor
... x = -14/3, -5/3
c. 9x² -48x +64 -3x² +8x = 0 . . . . . subtract the right side
... 6x² -40x +64 = 0 . . . . . . . . . . . . collect terms
... 3x² -20x +32 = 0 . . . . . . . . . . . . factor out 2
... (3x -8)(x -4) = 0 . . . . . . . . . . . . . . factor
... x = 8/3, 4
Tiffany answered 90% of the questions on her math test correctly. There were 50 questions on the test. how many questions did Tiffany answer correctly?
Multiply the total number of questions by the percent:
50 questions x 90% =
50 x 0.90 = 45
She answered 45 questions correctly.
Select Linear or Nonlinear for each function. Function Linear Nonlinear y=5x+1 y=23 y=1−2x2
The correct classification for each function is as follows:
1. [tex]\( y = 5x + 1 \)[/tex] - Linear
2. [tex]\( y = 23 \)[/tex] - Linear
3. [tex]\( y = 1 - 2x^2 \)[/tex]- Nonlinear
A linear function is one that can be written in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( x \)[/tex] is the independent variable. The graph of a linear function is a straight line.
1. For the function [tex]\( y = 5x + 1 \)[/tex], we can see that it is already in the form of a linear equation with [tex]\( m = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]. Therefore, this function is linear.
2. The function [tex]\( y = 23 \)[/tex] is a constant function. Although it does not have an [tex]\( x \)[/tex] term, it can still be considered linear because it can be written as [tex]\( y = 0x + 23 \)[/tex], where the slope [tex]\( m = 0 \)[/tex] and the y-intercept [tex]\( b = 23 \)[/tex]. The graph of this function is a horizontal line, which is a special case of a linear function.
3. The function [tex]\( y = 1 - 2x^2 \)[/tex] contains an [tex]\( x^2 \)[/tex] term, which makes it a quadratic function. Quadratic functions are nonlinear because their graphs are parabolas, not straight lines. The presence of the [tex]\( x^2 \)[/tex] term means that the rate of change of [tex]\( y \)[/tex] with respect to [tex]\( x \)[/tex] is not constant, which is a key characteristic of nonlinear functions. Therefore, this function is nonlinear.
Just number 9 not the other one please help
Answer:
I do believe the answer is C
Step-by-step explanation:
.004 / .0004 =
Answer:
c 10
Step-by-step explanation:
If we want to know how much bigger object A is than object B is we take object A and divide it by object B
object A 4 * 10^-3
----------- = -------------
Object B 4 * 10 ^-4
When dividing exponents with the same base
We can subtract them. The numbers out front get divided
4/4 * 10 ^ (-3- -4)
1 * 10 ^(-3+4)
1 * 10 ^1
10
Which transformation maps the strip pattern onto itself pdpd
half-turn
Step-by-step explanation:There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.
_____
Comment on other choices
Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.
Answer:
A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns
Step-by-step explanation:
Hope this helps :) -Mark Brainiest Please :)
The function y = –16t2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
Question 7 options:
0.25 seconds
5.51 seconds
11.02 seconds
7.79 seconds
5.51 seconds
Step-by-step explanation:y = 0 when the stone hits the ground. At that point, t can be found from ...
... 0 = -16t^2 +486
... 0 = t^2 -30.375 . . . . divide by -16
... 30.375 = t^2 . . . . . . add the opposite of the constant
Take the square root to get ...
... √30.375 = t ≈ 5.51 . . . . seconds
A silicon chip is 14 nanometers thick. A nanometer is equal to 0.000000001 meter. Express the thickness of the chip using scientific notation.
Answer:
1.4 × 10^-8
Step-by-step explanation:
The chip is 14 nanometers
14 * .000000001
.000000014
Move the decimal 8 places to the right, because we need 1 number in front of the decimal for scientific notation. The exponent will be -8 because we moved it 8 places to the right
1.4 × 10^-8
The thickness of the silicon chip in scientific notation is 1.4 x 10^-8 m.
Explanation:To express the thickness of the silicon chip in scientific notation, we need to convert the given thickness of 14 nanometers to meters.
Since 1 nanometer (nm) is equal to 0.000000001 meters, we can convert 14 nanometers to meters by multiplying it by the conversion factor:
14 nm x 0.000000001 m/nm = 0.000000014 m
Now, we can express the thickness of the chip in scientific notation:
0.000000014 m = 1.4 x 10-8 m
As a promotion, a clothing store draws the name of one of its customers each week. The prize is a coupon for the store. If the winner is not present at the drawing, he or she cannot claim the prize, and the amount of the coupon increases for the following week's drawing. The function f(x) = 20 (1.2)^x gives the amount of the coupon in dollars after x weeks of the prize going unclaimed. {{ x is the exponent on (1.2). }}
(A) What is the percent increase each week?
(B) What is the original amount of the coupon? (the initial value)
(C) What is the amount of the coupon after 2 weeks of the prize going unclaimed?
(D) After how many weeks of the prize going unclaimed will the amount of the coupon be greater than $100?
The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.
Which equation has the same solution as this equation? x^2-16x+12=0
Another equation that shares the same solutions as x²-16x+12=0 is 2x² - 32x + 24 = 0. This equation is the initial equation multiplied by 2 and thus would produce the same solutions when the quadratic formula is applied.
Explanation:The equation given is a quadratic equation, which is in the form ax²+bx+c = 0. The solutions of a quadratic equation are given by the formula: -b ± √b² - 4ac / 2a. This formula can be used to find the solutions of any other quadratic equation. For the given equation, x²-16x+12=0, the values of a, b, and c are 1, -16, and 12 respectively. So, another equation with the same solutions could be 2x² - 32x + 24 = 0. This equation has the same solutions because it's simply the initial equation multiplied by 2, so this doesn't change the results of the quadratic formula.
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On the main street, the tourists walked for s km with a speed of v km/hour. On the side road, the tourists walked twice the distance that they covered on the main street. How much time t (in hours) did the tourists spend if it is known that on the side road they walked with a speed that was 2 km/hour less than their speed on the main road? Find t when s=10, v=6.
Answer:
6 2/3 hours
Step-by-step explanation:
We assume the time of interest is the total time spent on the main road and side road.
In each case, ...
... time = distance/speed
On the main road, ...
... tmain = s/v
On the side road, ...
... tside = (2s)/(v -2)
Then the total time spent is ...
... ttotal = tmain + tside
... = s/v + (2s)/(v -2)
For s=10 and v=6, this is ...
... ttotal = 10/6 + 2·10/(6 -2) = 5/3 + 20/4 = 5/3 + 5 . . . . hours
... ttotal = 6 2/3 hours
Answer:
6 hr 40 min
Step-by-step explanation:
The amount, A, in milligrams, of radioactive material remaining in a container can be modeled by the exponential function A(t)=5(0.5)^0.25t where T is time, in years. Based on this model how many years does it take for half of the original radioactive material to be left remaining?
Answer:
4 years
Step-by-step explanation:
The exponent of 0.5 is 1 when t=4. So, half the original amount will be remaining when t=4.
Please help me with this one
How much water must be evaporated from 20 gallons of a 10% salt solution in order to obtain a 20% salt solution?
Answer:
8 gallons have to be evaporated to have a 20% salt solution.
hope this helped :)
Step-by-step explanation:
.10*20=2 gallons of salt.
That leaves 18 gallons of water.
.2x=2
x=2/.2
x=10 gallons after evaporation.
18-10=8
To obtain a 20% salt solution from a 10% salt solution, 20 gallons of water must be evaporated.
Explanation:To obtain a 20% salt solution from a 10% salt solution, the amount of water that needs to be evaporated can be calculated using a proportion. First, convert the percentages to decimals by dividing them by 100. Let x be the amount of water to be evaporated. The amount of salt in the initial solution is 10% of 20 gallons, or 0.10 * 20 = 2 gallons. The resulting solution will have 20% salt in a total volume of 20 - x gallons. Set up a proportion:
(2 gallons)/(20 gallons) = (0.20 * (20 - x) gallons)/(20 - x gallons)
Cross multiply and solve for x:
2(20 - x) = 0.20(20 - x)
Now solve the equation:
40 - 2x = 4 - 0.20x
2x - 0.20x = 40 - 4
1.8x = 36
x = 36/1.8
x = 20
Therefore, 20 gallons of water must be evaporated from the initial 20-gallon solution to obtain a 20% salt solution.
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I need help on this. The portrait studio can buy photographs on canvas. The small canvas photograph print is $20 and the large canvas photograph is $45. The studio wants to sell twice as many small prints as large prints. The studio also has to make at least $510 total to cover the costs of printing. How many of each type does the studio need to sell?
Numerical Reasoning
Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...
... 2×$20 +45 = $85
To have revenue of at least $510, the studio must sell ...
... $510/$85 = 6
sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.
_____
With an equation
Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...
... 20·2x +45·x ≥ 510
... 85x ≥ 510
... x ≥ 510/85
... x ≥ 6
The studio needs to sell at least 6 large prints and 12 small prints.
Which relation is displayed in this table? x y
5 5
A. {(5, 5), (6, −6), (8, 7), (−9, 9)} 8 7
6 -6
-9 9
B. {(5, 5), (−6, 6), (7, 8), (9, −9)}
C. {(−5, 5), (−6, 6), (−8, 7), (−9, 9)}
D. {(5, −5), (6, −6), (8, −7), (9, −9)}
A. {(5, 5), (6, −6), (8, 7), (−9, 9)}
Step-by-step explanation:Compare the table contents to the ordered pairs in each relation. The first pair of table values, (5, 5) matches relations A and B, but not C or D.
The second pair of table values (8, 7), matches relation A, but not B. Since all pairs of table values show up in relation A, and we have rejected relations B, C, and D as inappropriate choices, the answer is A.