Answer: B
Step-by-step explanation:
on edg
Ciara solved the exponential equation 3x+1 = 15 and her work is shown below. What is the first step she did incorrectly?
Step 1: log 3x+1 = log15
Step 2: (x + 1)log 3 = log15
Step 3: log3 = log 15 over x plus 1
Step 4: 0.477121 = 1.176091 over x plus 1
Step 5: 0.477121(x + 1) = 1.176091
Step 6: x + 1 = 1.176091 over 0.477121
Step 7: x + 1 = 2.464975
Step 8: x = 1.464975
(I think it is Step 3)
The sum of two numbers is 48. If one third of one number is 5 greater than one sixth of another number, which of the following is the smaller number?
6
22
26
42
please just tell me the answer.
Answer:
b: 22
Step-by-step explanation:
Convert the function into intercept form. Show your work. y=-x^2+5x+36
Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that
the distance from one corner to the mid point of a non-adjacent edge is a
minimum ...?
To optimize the dimensions of a rectangle with an area of 32 square cm such that the distance from one corner to the midpoint of a non-adjacent edge is minimized, one must use the Pythagorean theorem and calculus. The minimum distance occurs when the rectangle is a square with sides measuring 4√2 cm.
Assume the rectangle's dimensions are length L and width W, with the given area 32 cm2 such that LW = 32. To minimize the distance (D) from one corner to the midpoint of the non-adjacent edge, we can use the Pythagorean theorem, given by D = √(L2 + (W/2)²).
Since the area is fixed, W can be expressed as 32/L, and we can write D as a function of L. After substituting 32/L for W and differentiating with respect to L, we can find the minimum by setting the derivative equal to zero and solving for L.
The minimum distance is achieved when the rectangle is a square, with length and width both equal to √32, which simplifies to 4√2 cm, which is approximately 5.66 cm for both dimensions.
The equation y=1.2x+8.9 is a linear model for data comparing the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y). About how much weight does a baby gain per month?
For all the people that actually have this question:
For babies between 1 and 11 months old, the equation y = 1.2x + 8.9 models the baby's weight when the baby is x months old. A baby in that age range weighs 17.5 lbs. What is the best estimate for the age of the baby?
Answer:
7 months
Step-by-step explanation:
1.2 * 7 + 8.9 = 17.3 & 17.3 is close to 17.5
I just took the test!
The weight that a baby gain per month is 1.2.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given is a linear equation,
y = 1.2x + 8.9
This equation compares the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y).
This equation is in the slope intercept form, where 1.2 is the slope and 8.9 is the y intercept.
Slope is the change in y coordinates by change in x coordinates.
So, weight baby gain per month is 1.2.
Hence 1.2 is the weight that the baby gain per month.
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A children's book has dimensions 20 cm by 24 cm.
What scale factor should be used to make an enlarged version that has dimensions 25 cm by 30 cm?
A. 5
B. 1.5
C. 1.25
D. 0.8
Answer:
We should use C. 1.25
Step-by-step explanation:
We know that the children's book dimensions are 20 cm x 24 cm
We need to find a scale factor (which is a number) that will turn the dimensions 20 cm x 24 cm ⇒ 25 cm x 30 cm
We can write :
(20 cm) . a = 25 cm
Where ''a'' is the scale factor.
Solving for a :
[tex](20cm).a=25cm\\a=\frac{25cm}{20cm}=1.25 \\a=1.25[/tex]
This result is reasonable because the scale factor won't have units
A scale factor of 1.25 turns 20 cm ⇒ 25 cm
We can use the another dimension to verify :
(24 cm) . a = 30 cm
(24 cm) . (1.25) = 30 cm
30 cm = 30 cm
The scale factor is option C. 1.25
a person can pay $9 for a membership to the Science Museum then go to the museum for $1 per visit.For a member of the science museum,what is the total cost of 10 visits?
For a member of the science museum, the total cost of 10 visits is equals to $19.
What is cost?" Cost is defined as the amount paid for any purchase something or using any services."
According to the question,
Membership cost per person to the Science Museum = $9
Per visit cost for a member = $1
'x' represents the number of visits
'y' represents the total cost
As per the condition we get,
y = 9 + $1x
Therefore,
Total cost of 10 visits ,
y = 9 + 1(10)
= 9 + 10
= $19
Hence, for a member of the science museum, the total cost of 10 visits is equals to $19.
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PLEASE HELP!! the measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angle?
The inverse of the function f(x) = 1/2x + 10 is shown.
h(x) = 2x – ?
What is the missing value?
Answer:
d. 20
Step-by-step explanation:
Replace the x and y values in the equation
(y = 0.5x + 10) to (x = 0.5y + 10)
Now, solve for the y value in the new equation. You'll get y = 2x + 20.
So, the intercept of the inverse function is 20.
You want to deposit $12,000 in a bank at an interest rate of 8 percent per year. What is the future value of this money after five years?
Answer: For Plato users the answer is
B . $ 17,631.94
Step-by-step explanation:
Which expression represents, six times a number plus 8 times a number?
6a + 8
6 + 8 + a + b
48(ab)
6a + 8b
The answer is 6a+8b, so *D*, hope it helps!
What is the slope of the line joining (5, 9) and (−2, 9)?
A. -7/4
B.-4/7
C.0
D.No slope
What is v in this formula v=3u 5t if u=5.1 and t=27.3 v?
Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets
What percentage of the £385 does Laura get ?
With working out
To find out what percentage of the £385 Laura gets, we need to determine the amounts that Kim and Molly get. By solving equations and subtracting their amounts from the total, we find that Laura gets approximately 45.45% of the £385.
Explanation:To find out what percentage of the £385 Laura gets, we need to first find out the amounts that Kim and Molly get. Let's assume that Kim gets x amount. According to the ratio, Molly gets 5x amount. From the information given, we know that Kim gets £105 less than Molly, so we can write the equation: 5x - x = £105. Solving this equation, we get x = £35. Therefore, Kim gets £35 and Molly gets 5x £35 = £175. Now, to find out the amount Laura gets, we subtract the amounts of Kim and Molly from the total amount: £385 - £35 - £175 = £175. So Laura gets £175. To find out the percentage, we divide the amount Laura gets by the total amount (£385) and multiply by 100: (175 / 385) * 100 = 45.45%. Therefore, Laura gets approximately 45.45% of the £385.
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A point is moving along the graph of a given function such that dx/dt is 2 centimeters per second. Find dy/dt for the given values of x.
y = 9x2 + 5
(a) x = -1
dy/dt =____ cm/sec
(b) x = 0
dy/dt =____cm/sec
(c) x = 3
dy/dt =_____ cm/sec
...?
The rates of change in y for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively by using the derivative dy/dt = 18*x*dx/dt.
Explanation:This problem is a case of related rates in calculus. Given that dx/dt is constant at 2 cm/sec and the function y = 9x2 + 5, we need to differentiate the function with respect to t to find dy/dt. Solving for dy/dt, you get dy/dt = 18x * dx/dt.
When x = -1, dy/dt = 18*-1*2 cm/sec = -36 cm/sec.When x = 0, dy/dt = 18*0*2 cm/sec = 0 cm/secWhen x = 3, dy/dt = 18*3*2 cm/sec = 108 cm/secSo, the rates of change in y with respect to time for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively.
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what are three equivalent fractions for 80/100 ...?
Three equivalent fractions for [tex]\( \frac{80}{100} \) are \( \frac{4}{5} \), \( \frac{160}{200} \), and \( \frac{400}{500} \)[/tex].
To find three equivalent fractions for [tex]\( \frac{80}{100} \)[/tex], we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 20 in this case.
1. Divide both the numerator and denominator by 20:
[tex]\[ \frac{80 \div 20}{100 \div 20} = \frac{4}{5} \][/tex]
So, [tex]\( \frac{80}{100} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
2. Multiply both the numerator and denominator by the same non-zero integer:
[tex]\[ \frac{80 \times 2}{100 \times 2} = \frac{160}{200} \][/tex]
So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{160}{200} \)[/tex].
3. Similarly, we can multiply both the numerator and denominator by another non-zero integer:
[tex]\[ \frac{80 \times 5}{100 \times 5} = \frac{400}{500} \][/tex]
So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{400}{500} \)[/tex].
a dragon traveled at a rate of 35 miles per hour for 2.5 hours .what distance did the dragonfly travel?
Water flowing from a faucet can fill 1/4 of a tank in 3 minutes. How long does it take to fill the tank completely with water?
Which expressions simplify to a rational answer?
A. √11 ⋅ √5
B. √9 ⋅ √16
C. 5√2 ⋅ √2
D. √3 ⋅ √2
Answer:
if your a k12 kid this is old and was once not a multip choice question but the answer is b
Step-by-step explanation:
-Former k12 kid
if 5^-x=3 what does 5^3x equal?
How many kg in 1 gram?
-x^2=23 in standard form
What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?
Answer: The required sum of first terms of the series is [tex]\dfrac{1705}{64}.[/tex]
Step-by-step explanation: We are given to find the sum of the first five terms of a geometric series with first term and common ratio as follows :
[tex]a_1=20~~~~~\textup{and}~~~~~r=\dfrac{1}{4}.[/tex]
We know that
the sum of first n terms of a geometric series with first term [tex]a_1[/tex] and common ratio r is given by
[tex]S_n=\dfrac{a(1-r^n)}{1-r}.[/tex]
Therefore, the sum of first 5 terms of the given geometric series is given by
[tex]S_5\\\\\\=\dfrac{a(1-r^5)}{1-r}\\\\\\=\dfrac{20(1-(\frac{1}{4})^5)}{1-\frac{1}{4}}\\\\\\=\dfrac{20\left(1-\frac{1}{1024}\right)}{\frac{3}{4}}\\\\\\=20\times\dfrac{4}{3}\times\dfrac{1023}{1024}\\\\\\=20\times\dfrac{341}{256}\\\\\\=\dfrac{5\times 341}{64}\\\\\\=\dfrac{1705}{64}.[/tex]
Thus, the required sum of first terms of the given geometric series is [tex]\dfrac{1705}{64}.[/tex]
If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13 people?
To convert from pounds to ounces, multiply the number of pounds by the unit equivalence of 1 pound = 16 ounces.
Conversion from pounds to ounces:
First, find the unit equivalence: 1 pound = 16 ounces.
Next, multiply the number of pounds by the unit equivalence. Thus, 5 pounds x 16 equals 80 ounces.
ricardo has a bag of mixed fruit snacks. in the bag, there are 8 cherry fruit snacks and 12 strawberry fruit snacks. what is the ratio of strawberry to cherry?
Consider the sequence 2, 5, 10, 17, ...
What is the value of a4?
2
5
10
17
Answer:
The answer is [tex]a4=17[/tex]
Step-by-step explanation:
we have the sequence
[tex]2,5,10,17,...[/tex]
Let
a1-----> the first term
a2----> the second term
a3----> the third term
a4----> The fourth term
In this problem we have
[tex]a1=2[/tex]
[tex]a2=5[/tex]
[tex]a3=10[/tex]
[tex]a4=17[/tex]
therefore
the answer is
[tex]a4=17[/tex]
If line segment AB = 12 feet, what is the length of line segment AC?
Select one of the options below as your answer:
A.
6 feet
B.
10 feet
C.
12 feet
D.
24 feet
give me an example of a unit rate used in a real world sutuation
All real numbers n that are less than -3
The set of all real numbers n that are less than -3 can be represented as: [tex]\[ \{ n \mid n < -3 \} \][/tex]
The set of real numbers less than -3 encompasses an infinite range of values extending to the left of -3 on the number line. These numbers are characterized by being smaller than -3, denoted as ( n < -3 ). In interval notation, this set is represented as (-∞, -3), indicating that it includes all real numbers from negative infinity up to, but not including, -3.
This set is unbounded, as there is no limit to how far left the numbers extend, encompassing an infinite continuum of values that are progressively smaller than -3.
. Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12.50 plus tax. Zalia pays for herself and her friend. They have lunch at the museum’s cafe. Zalia has a sandwich for $5.95, an apple for $1.25 and a drink for $1.69. She is charged tax and also tips her server 15%. If tax is 7.25%, how much did Zalia pay all total for her day at the science museum?
a.
$41.43
b.
$37.68
c.
$36.35
d.
$24.27
The total comes to $37.67, so the closest answer is (b) $37.68.
We will calculate how much Zalia paid for her day at the science museum including admission fees, lunch, and the tax and tip for both of these.
Firstly, let's calculate the total cost of admission for Zalia and her friend:
Admission for one person: $12.50
Admission for two people: $12.50 x 2 = $25.00
Now, let's find the total cost of Zalia's lunch:
Sandwich cost: $5.95
Apple cost: $1.25
Drink cost: $1.69
Total lunch cost before tax and tip: $5.95 + $1.25 + $1.69 = $8.89
Next, we add the tax:
Tax for admission: $25.00 x 7.25% = $1.81
Tax for lunch: $8.89 x 7.25% = $0.64
Total tax: $1.81 + $0.64 = $2.45
Now, we calculate the tip for the lunch:
Tip: $8.89 x 15% = $1.33
Finally, add everything up to get the total amount Zalia paid:
Total cost without tax and tip: $25.00 + $8.89 = $33.89
Total tax and tip: $2.45 + $1.33 = $3.78
Grand total: $33.89 + $3.78 = $37.67
Examining the provided options, we can see that the closest amount to our calculation is $37.68, considering the possibility of a rounding difference in the final tax and tip calculations. Thus, the correct answer is (b) $37.68.