Answer:
(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
Step-by-step explanation:
The equation for exponential growth can be written in the form ...
f(t) = a·b^t
where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...
b = 1 +r . . . . . where r is the growth rate in time period t
__
banana breadThe equation for the area of mold on the banana bread is given as ...
B(t) = 20·1.06^t
Comparing to our generic equation, we see ...
a = 20b = 1.06 = 1 + 0.06The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.
__
whole wheat breadWe are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.
W(1) = 40.8 = a·b^1
W(4) = 43.30 = a·b^4
The ratio is ...
W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8
Then the value of b can be found to be ...
b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02
The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.
__
comparison of growth ratesThe mold growth rate on the banana bread compared to that on the whole wheat bread is ...
(banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3
We can conclude ...
The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
4, 5, 5, 6, 7, 8, 8,9
What is the range?
Sally makes $3,000 each month. What is the most she can spend on housing?
Following the 30% rule of thumb, Sally should only spend a maximum of $900 on her rent
Numbers and percentageGiven Data
Monthly Salary = $3000Percentage spent on rent = 30%Let us find 30% of $3000
= 30/100* $3000
= 0.3*$3000
= $900
Learn more about percentages here:
https://brainly.com/question/24304697
SPJ1
Evaluate the limit. lim x → 0 4ex/2 − 4 − 2x − 1 2 x2 x3
The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Limit of the function
The limit of the given expression is calculated as follows;
lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³]
= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)
= (4)/2 - 4
= 2 - 4
= - 2
Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Learn more about limits here: https://brainly.com/question/251701
#SPJ1
Agnes who loves adventure tries to jump towards Gru who is sitting motionless on a raft with negligible mass. He tries to catch the 30 kg Agnes who is running 1.2 m/s towards him. As he caught Agnes, the motionless raft started to move. How heavy is Gru if the raft started to move with a speed of 0.5 m/s? (Note: Include correct units and sign. Ex. "20 kg*m/s" , "20 N*s" , "20 kg")
By conservation of momentum, we will see that the mass of Gru is 32 kilograms.
How heavy is Gru?
Here we need to use the conservation of momentum.
Initially, Gru is stop, and Agnes with a mass of 30kg has a velocity of 1.2 m/s, so the total initial momentum is:
P = 30kg*1.2m/s = 36 kg*m/s.
At the end, the total mass is M, the mass of Gru, plus the mass of Agnes:
(M + 30kg).
And the final speed is 0.5 m/s, then the final momentum is:
P' = (M + 30kg)*0.5m/s
And the final momentum must be equal to the initial momentum:
36 kg*m/s = (M + 30kg)*0.5m/s
Now we can solve that for M:
( 36 kg*m/s)/(0.5 m/s) = M + 30kg
72kg = M + 30kg
72kg - 30kg = 32 kg = M
The mass of Gru is 32 kilograms.
If you want to learn more about momentum:
https://brainly.com/question/7538238
#SPJ1
DEF, DF = 16 and m angle F = 45
Answer: [tex]8\sqrt{2}[/tex]
================================================
Work Shown:
x = length of each leg
Use the pythagorean theorem to get...
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = 16^2\\\\2x^2 = 256\\\\x^2 = 256/2\\\\x^2 = 128\\\\x = \sqrt{128}\\\\x = \sqrt{64*2}\\\\x = \sqrt{64}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
Or as an alternative path, you can divide the hypotenuse by [tex]\sqrt{2}[/tex] and then rationalize the denominator.
Both of these methods apply to 45-45-90 triangles only.
Answer:
[tex]8\sqrt{2}[/tex]
Step-by-step explanation:
We can sum the angles in a triangle to 180°:
m<D + m<E + m<F = 180°
m<D + 90° + 45° = 180°
m<D = 45°
Therefore, the triangle is an isosceles right triangle, since the base angles, <F and <D are the same measure. Because the triangle is isosceles, the legs are congruent, meaning that
DE = EF
We can use the Pythagorean Theorem([tex]a^{2} + b^{2} = c^{2}[/tex]) and plug in 16 as c, and DE and EF as a and b:
[tex]DE^{2} + EF^{2} = 16^{2}[/tex]
Since DE is the same as EF, we can substitute it in:
[tex]DE^{2} + DE^{2} = 256\\2DE^{2} = 256\\DE^{2} = 128\\DE = \sqrt{128}[/tex]
The square root of 128 is the same as [tex]8\sqrt{2}[/tex] since 128 can be factored into 64 x 2. So [tex]8\sqrt{2}[/tex] is the answer.
If you are looking for an easier way to do this, once you are able to recognize DEF is an isosceles triangle, you can say [tex]DE \times \sqrt{2} = 16[/tex] as this applies to all isosceles right triangles. This simplifies to:
[tex]DE = \frac{16}{\sqrt{2}} \\DE = \frac{16}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2} } \\DE = \frac{16\sqrt{2} }{2} \\DE = 8\sqrt{2}[/tex]
I’LL GIVE BRAINLIST IF YOU ANSWER CORRECT:
Answer:
Step-by-step explanation:
Solution
The first step is to simplify the top of the fraction. Subtract 5.6 - 2.7
The numerator (top) and denominator(bottom) are decimal fractions. They are 2.9 for the top and 2.9 for the bottom.
The whole expression reduces down to 1, which is an integer.
Note
You have choices. If you want exact answers you will have to list those choices.
Answer: 1
HELP!!! PLEASE HURRY!!!!
Answer:
B, I solved then used interval notion to convert it.
Answer:
the answer is b
Answer:
the answer is b
If x = 2y = 3
find xy-y+ x × x
Answer:
here ....x = 2 and y = 3
[tex] = xy - y + x \times x[/tex]
[tex] = 2 \times 3 - 3 + 2 + 2 \times 2[/tex]
[tex] = 6 - 3 + 2 + 4[/tex]
[tex] = 12 - 3[/tex]
[tex] = 9[/tex]
A triangle is placed in a semi circle with a radius of 9 mm find the area of the shaded region of the semi circle (not including the triangle)
The area of the shaded region will be 46.17 ft.²The number of unit squares that cover the surface of a closed-form is the figure's area.
What is the area?
The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Semicircle radius , r = 9 ft.
The height of the triangle, h=r=9 ft
The triangle is located where it is inscribed in the semicircle. The diameter of the semicircle is given as b, the base length of the triangle.
The diameter of the semicircle = 2 × The radius of the semicircle
D=2r
D= 2 × 9 ft
D= 18 ft.
Triangle base length,b = D= 18 ft.
The area of the triangle is found as;
[tex]\rm A= \frac{1}{2}bh \\\\ A = \frac{1}{2} \times 18 ft. \times 9 ft. \\\\ A = 81 \ ft^2[/tex]
[tex]A_{semi}={\rm \frac{A_{circle}}{2}} \\\\ A_{semi}= \frac{\pi \ r^2}{2}\\\\\ A_{semi}= \frac{3.14 \times 9^2}{2} \\\\ A_{semi} = 127.17 ft^2[/tex]
The area of the shaded region is;
a= 127.17 ft.² - 81 ft.²
a = 46.17 ft.²
Hence,the area of the shaded region will be 46.17 ft.²
To learn more about the area, refer to the link;
https://brainly.com/question/11952845
#SPJ1
Which of the following statements are true?
The prime factorization of 21 is 3 x 7.
The LCM of 14 and 21 is 42.
The prime factorization of 14 is 2 x 7.
14 is a composite number.
21 is a prime number.
The GCF of 14 and 21 is 14.
Answer:
The prime factorization of 14 is 2 x 7.
Step-by-step explanation:
The prime factorization of 14 is 2 x 7.
Answer:
14 is a composite number
Step-by-step explanation:
Select the expressions whose value is 4.
0(-2)²
02(-2)
0-4÷2
0-41
Answer: The correct answer is A, [tex](-2)^{2}[/tex].
Step-by-step explanation:
A negative multiplied with another negative is a positive. Squaring is multiplying an integer by itself. Thus, it would look like -2×-2, which is equal to 4. I hope this helps!! :)
Julia is in charge of buying clothing in bulk for a sporting goods store. The table shows the unit prices of the items she intends to buy.
Unit Prices of Clothing Items for a Sporting Goods Store
Item
Unit Price
T-shirts
$7.50
Shorts
$9.00
Windbreakers
$12.25
If she will buy 35 T-shirts, 45 pairs of shorts, and 25 windbreakers, what will be her total cost?
$958.75
$973.75
$1,021.25
$1,038.75
The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers is $973.75.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Cost of 1 T-shirt = $7.50
Cost of 35 T-shirts = 7.50 x 35
= 262.5
Cost of 1 Shorts = $9.00
Cost of 45 T-shirt = 9.00 x 45
= 405
Cost of 1 windbreakers = $12.25
Cost of 25 windbreakers = 12.25 x 306.25
So, The total cost of 35 T-shirts, 45 pairs of shorts, and 25 windbreakers
= 262.5+405+306.25
= $973.75
Hence Her total cost is $973.75.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ1
State your conclusion in the form of a theorem, and then prove the theorem using a two-column proof. When you write the proof, refer to the diagram you created in part A. It will be helpful to use point labels to state what is given and what you have to prove and to use those labels throughout the proof.
As part of the proof, you’ll have to construct a line segment connecting the top intersection point on one of the transversals with the lowest intersection point of the other transversal, thus forming two triangles. Take a screenshot of the construction, save it, and insert the image in the space below before you begin your written proof.
The midpoint theorem simply states that the line segment that joins the two sides of the triangle is parallel to the third side.
How to illustrate the theorem?Your information is incomplete. Therefore, an overview of the theorem will be given. It should be noted that the midpoint theorem states that the line drawn through the mid point of one side of the triangle is parallel to another side.
To find the midpoint, one can measure the distance between the two end points and divide the results by 2.
Learn more about theorem on:
https://brainly.com/question/343682
#SPJ1
Helppp me pleaseeeee
NO LINKS!!
Solve the compound inequality. Write the solutions in interval notation.
x + 7 ≥ 4 and 11x - 8 ≥ 3
Answer: [1, infinity)
===========================================================
Explanation:
Let's isolate x in the first inequality mentioned.
x + 7 ≥ 4
x + 7-7 ≥ 4-7
x ≥ -3
I subtracted 7 from both sides to undo the +7.
Now isolate x in the second inequality. We first add 8 to both sides, then divide both sides by 11.
11x - 8 ≥ 3
11x - 8+8 ≥ 3+8
11x ≥ 11
11x/11 ≥ 11/11
x ≥ 1
------------------
The two solutions we found were
x ≥ -3 and x ≥ 1
Next, draw out a number line with closed circles at -3 and 1. Shade to the right of each closed circle endpoint as you see below.
Notice that the two inequalities overlap for x ≥ 1
In other words, if a number is -3 or larger AND 1 or larger, then the number is 1 or larger.
The two solutions intersect to form x ≥ 1
The inequality x ≥ 1 is the same as 1 ≤ x which is the same as 1 ≤ x < infinity
Then that turns into the interval notation of [1, infinity)
The square bracket includes the endpoint 1.
If needed, use the infinity symbol in place of the word "infinity".
Answer:
[1, ∞)
Step-by-step explanation:
To solve a compound inequality, first separate it into two inequalities and solve them separately:
Solution of Inequality 1:
x + 7 ≥ 4
⇒ x ≥ 4 - 7
⇒ x ≥ -3
Solution of Inequality 2:
11x - 8 ≥ 3
⇒ 11x ≥ 3 + 8
⇒ 11x ≥ 11
⇒ x ≥ 1
As both graphs overlap for x ≥ 1, this is the solution.
Therefore, in interval notation: [1, ∞)
Adrian's annual salary is $111,000. He is not eligible for a Roth IRA because he makes
too much money. His company offers a matching program that is 1:1 up to 3% of annual
salary. (do not include commas or dollar signs in your answers)
How much should he contribute to Roth IRAS?
If he is not eligible for Roth IRAs, then he cannot contribute to Roth IRAs. However, he can contribute $3,330 monthly under his company's Matching Program.
What is a Roth IRA?The Individual Retirement Account to which employees in the United States can contribute after-tax earnings is called the Roth IRA.
Under its governing principles, certain individuals whose annual income exceeds stipulated amounts are INELIGIBLE to contribute.
How do we arrive at $3,330?Recall that the question indicates that his company offers a matching program with a ratio 1:1 up to 3% of his annual salary.
Since his annual salary is $111, 000,
3% x 111,000 = 3,330.
This means that annually, the total matching contribution due to Adrian would be:
3,330 x 2 = 6, 660.
Learn more about Roth IRA at:
https://brainly.com/question/1300867
#SPJ1
N(-2,-2) after a 90 degree counterclockwise rotation
Answer: (2,-2)
Step-by-step explanation:
Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)
What are the solutions to 3(x + 2)(x - 9) = 0?
Select all that apply.
2
-9
-2
-3
9
Answer:
(3)+1. 12-2=9+1 so 9 is the answer
A music club has $187 to buy ice cream for a party. Each carton of ice cream costs $4. If the club buys as many cartons as possible, how much money will the club have left?
Answer:
They would have $3 dollars left over.
Step-by-step explanation:
If you divide 187 by 4, you get 46.75. But if you look again, you can see that the remainder is 3 and it can confirm that it is the left over money that the club has now after buying as many ice cream cartons as possible.
A) all values at which h has a local maximum
B ) all local maximum values of h
For the given function h(x), we have:
a) at x = -2 and x = 2.
b) y = 0 and y = 3.
How to identify the maximums of function h(x)?
First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.
By looking at the horizontal axis, we can see that the maximums are at:
x = -2 and at x = 2.
Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.
The first maximum value is at y = 0 (the one for x = -2)The second maximum is at y = 3 (the one for x = 2).If you want to learn more about maximums:
https://brainly.com/question/1938915
#SPJ1
which graph represents the linear function y=-5x+2?
Answer:
The second picture is the correct answer the graph must be decreasing..
Step-by-step explanation:
The second picture is the correct answer the graph must be decreasing..
Solve 10x-4y=15 for y.
Answer:
y = 15/-4 + 2.5x
Step-by-step explanation:
10x - 4y = 15
-4y = 15 - 10x
y = 15/-4 + 2.5x
Apply the indicated operations to the matrix; then choose the correct answer.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The correct option is B.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
When the indicated operation 4R₁ → R₁ is applied then the matrix will be,
[tex]\left[\begin{array}{ccc}1&2&0\\-2&-1&3\end{array}\right] \rightarrow \left[\begin{array}{ccc}4&8&0\\-2&-1&3\end{array}\right][/tex]
Hence, the correct option is B.
Learn more about Multiplication:
https://brainly.com/question/14059007
#SPJ1
Convert 65,000,000 to scientific notation
Answer:
6.5 x 10^7
Step-by-step explanation:
give brainliest, please!
hope this helps :)
solve
16x+8>=12x+20
A. x<=3
B. x<=7
C. x>=3
D. x>=7
Answer: C
Step-by-step explanation:
[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]
The graph shown below expresses a radical function that can be written in the form f(x) = a(x + k)^1/n + c. What does the graph tell you about the value of a in this function?
Answer:
Graphs can be used to represent functions
The value of a is less than 0.
The function is given as:
The parent function of f(x) is:
So, by comparison:
The function becomes:
Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)
So, we have:
Substitute these values in
So, the function becomes
From the graph, we have the following point;
So, the function becomes
Subtract 2 from both sides
Square both sides
Divide both sides by -9
So, we have:
-1 is less than 0.
Hence, the value of a is less than 0.
Step-by-step explanation:
Answer:
The value of a in this function is 0
Step-by-step explanation:
The given function is
[tex]f(x) = a(x + k)^\frac{1}{n} + c.[/tex]
Here , f(x) is y = [tex]x^{\frac{1}{2} }[/tex] So , n = 2.
By substituting the value we get the function :
[tex]f(x) = a(x + k)^\frac{1}{2} + c.[/tex]
The vertex of the graphs are : (k, c) = (-5 ,2)
The function becomes:
[tex]f(x) = a(x + 5)^\frac{1}{2} + 2[/tex]
The following point on the graph shows : (x, y) = (-4 , 5)
The function becomes:
[tex]5 = a(-4+ 5)^\frac{1}{2} + 2\\5 = a(-9)^\frac{1}{2} + 2\\\\\3 = a(-9)^{\frac{1}{2} }(Subtract 2 from both side )\\\\9 = a (-9) ( Square both sides) \\\\-1 =a ( Divide both side by -9)\\[/tex]
a = -1
Here , -1 is less than zero
Hence , the value of a is less than o.
For more function related doubts visit:https://brainly.com/question/9834848
#SPJ1
HELPP (NO LINKS)
The table shows the value of a townhome for 3 years after it is purchased. The values
form a geometric sequence. If the pattern continues, how much will the townhome be
worth after 7 years?
The amount that the home will be worth after 7 years is $457763.67
The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:
Tn = ar^n-1
where
a is the first term = 120,000
r is the common ratio = 150000/120000 = 1.25
Required
7th term
Substitute
T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6
T7 = 120,000(3.8147)
T7 = $457763.67
Hence the amount that the home will be worth after 7 years is $457763.67
Learn more on geometric sequence here: https://brainly.com/question/1509142
#SPJ1
Answer:
(c) $457,763.67
Step-by-step explanation:
hope this helps:)
The formula for calculating percentage marckup is :
A. sticker price - invoice price/invoice price • 100 = percent markup
B. sticker price - invoice price/invoice price • 100 = markup
C. Invoice price - sticker price/sticker price • 100 = percent markup
D. Invoice price - sticker price/invoice price • 100 = percent markup
The formula for calculating the mark up percentage is as follows:
sticker price - invoice price/invoice price • 100 = percent mark up
How to find the percentage mark up?Percentage mark up can be described as follows:
percentage mark up = selling price per unit - cost price per unit / cost price per unit × 100
Therefore,
Mark up is the difference between a product's selling price and cost as a percentage of the cost.
Therefore, the formula for calculating the mark up percentage is as follows:
sticker price - invoice price/invoice price • 100 = percent mark up
learn more on percentage mark up here: https://brainly.com/question/16959984
#SPJ1
Math need help please
Rewrite the expression as a product of four linear factors:
(x² – 3x)² – 14(x² – 3x) + 40
-
Answer:
Submit Answer
[tex]~~(x^2 -3x)^2 -14(x^2 -3x) +40\\\\=u^2-14u+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Let}~ u = x^2 -3x]\\\\=u^2 - 10u-4u +40\\\\=u(u-10)-4(u-10)\\\\=(u-4)(u-10)\\\\=(x^2 -3x -4)(x^2 -3x -10)~~~~~~~~~~~~~;[\text{Substitute back}~ u = x^2 -3x]\\\\=(x^2 -4x+x-4)(x^2 -5x+2x-10)\\\\=\textbf{[}x(x-4) +(x-4) \textbf{]} \textbf{[}x(x-5) +2(x-5) \textbf{]} \\\\=(x+1)(x-4)(x+2)(x-5)[/tex]