Answer:
Step-by-step explanation:
To find the base of the exponential function F(x) = b^x, we need to use the information that its graph contains the point (1/3, 2). We can use this information to solve for b.
Since the graph passes through the point (1/3, 2), we can set x = 1/3 and y = 2 in the equation F(x) = b^x:
b^(1/3) = 2
Taking the cube root of both sides, we get:
b = (2)^3 = 8
So the base of the exponential function F(x) = b^x is b = 8, which means the correct answer is C) 8.
Help!!
Write an equation to show the total cost, y, for x months.
YOU WIL GET BRAINLIEST!!
The equation to represent the total cost, y, for x months is y = 12x + 30.
From the given table, we can observe that the total cost increases by $12 for each additional month of usage.
This means that the rate of change, or the slope of the equation, is $12 per month.
We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.
Putting it all together, the equation to represent the total cost, y, for x months is:
y = 12x + 30
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I will give brainliest and ratings if you get this correct
The quotient rule is proved below.
What is derivative of a function?In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Given is the expression -
Q(x) = F(x)/G(x)
Quotient rule -Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -
f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Proof -Now, let f(x) = u(x) and g(x) = v(x).
Q(x) = u(x)/v(x)
Q(x) = u(x) v⁻¹(x)
Using the product rule -
Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}
Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)
Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)
Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Therefore, the quotient rule is proved above.
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Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that
cost $6.50 per pound with French Roast Columbian coffee that cost $8.20 per pound to make a 34-pound
blend. Their blend should cost them $6.90 per pound. How much of each type of coffee should they buy?
Pounds of City Roast coffee =
Pounds of French Roast coffee =
Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:
Pounds of City Roast coffee = 26Pounds of French Roast coffee = 8.What is a system of equations?A system of equations is two or more equations solved concurrently or at the same time.
A system of equations can also be described as simultaneous equations.
The cost per pound of City Roast Columbian coffee = $6.50
The cost per pound of French Roast Columbian coffee = $8.20
The total quantity of the blend = 34 pounds
The cost per pound of the blend = $6.90
The total cost of the 34 pounds = $234.60 ($6.90 x 34)
Let the number of pounds of City Roast coffee = x
Let the number of pounds of French Roast coffee = y
Equations:x + y = 34 ... Equation 1
6.5x + 8.2y = 234.6 ... Equation 2
Multiply Equation 1 by 6.5:
6.5x + 6.5y = 221 ... Equation 3
Subtraction Equation 3 from Equation 2:
6.5x + 8.2y = 234.6
-
6.5x + 6.5y = 221
1.7y = 13.6
y = 8
Substitute, y = 8 in Equation 1:
x + y = 34
x = 34 - 8
x = 26
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Sara can type 90 words in
4 minutes. About how many words
would you expect her to type in
10 minutes at this rate?
[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]
A true-false quiz contains six questions. In how many ways can a student answer the questions if the student answers two of the questions with "false" and the other four with "true"?
Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.
Step-by-step explanation:
NEED ANSWER ASAP PLEASE! THANK YOU
The y-coordinate of point P is 16/3, which rounded to two decimal places is approximately 5.33.
What is the y-coordinate of PFirst, we need to find the coordinates of point P. Since point P partitions the directed segment AB in the part-to-part ratio of 2:4, we can use the following formula to find its coordinates:
P = (4A + 2B) / 6
Substituting the coordinates of A and B, we get:
P = (4(5,7) + 2(1,-6)) / 6
P = (20,28) + (2,-12) / 6
P = (22,16) / 6
P = (11/3, 16/3)
y-value = 5.33
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Elmo wrote Kris a check for $601.73, and Kris deposited the check into her checking account. Where was Kris' signature?
A. On neither the front of the check nor the back of the check
B. On both the front of the check and the back of the check
C. Only on the back of the check
D. Only on the front of the check
The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.
C. Only on the back of the check
What is a checking account?A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.
The amount of check Elmo wrote Kris = $601.73
The amount Kris deposited into her checking account = The check Elmo issued to her
The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified check is to be deposited into the checking account.
The correct option is therefore option C.
C. Only on the back of the check
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50 pair of tennis shoes at $85 a pair with terms 4/10, 2/30, n/60. the invoice was dated for october 15. payment was sent in october 28, what was the total amount of the check
Answer:
Step-by-step explanation:
The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.
Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.
The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.
Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.
What is the perimeter of parallelogram WXYZ?
The perimeter is ]- (Type an integer or a decimal.)
The perimeter of the parallelogram is; 184
What is the perimeter of the parallelogram?In geometry, the perimeter of a shape is defined as the total length of its boundary.
Now, from the given image, we don't know the vertical sides XW and YZ and we can find it from Pythagoras theorem;
XW = √(68² - 60²)
XW = 32
Thus, the perimeter of the parallelogram is;
Perimeter = 2(32 + 60)
= 2 * 92
= 184
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Complete the sentence below.
0.075 is a hundred times smaller than
Answer:
0.0075
Step-by-step explanation:
In a fair out of 5 people 2 are men and 2 are women and the remaining are children there are 2500 people at the fair. what percentage of people are adult?
Answer:
Percentage of adults = 80%
Number of adults = 2000
Step-by-step explanation:
Percentage of men = 2/5 x 100 = 40%
Percentage of women = 2/5 x 100 = 40%
Percentage of adults = 40+ 40= 80%
If there are 2500 people, then number of adults
= 2500 x 80%
= 2500 x 80/100
= 2000 adults
A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring 3 cm, 4 cm, and 5 cm, and angles measuring 37°, 53°, and 90°. To create the actual sign shown, the drawing must be dilated using a scale factor of 80.
Answer:
240 cm, 320 cm, 400 cm
Step-by-step explanation:
The drawing length multiplied by the scale factor gives the real length.
3 cm × 80 = 240 cm
4 cm × 80 = 320 cm
5 cm × 80 = 400 cm
Answer: 240 cm, 320 cm, 400 cm
The length of a rectangle is 6 cm. less than 3 times the width. If the perimeter of the rectangle is 60 cm.,
find the length and the width.
(Hint - The perimeter of a rectangle is given by: P = 2L+2W)
The length is
The width is
cm.
Submit Question
cm.
Question Help: Post to forum
Answer: w=9cm l=21cm
Step-by-step explanation
l=3w-6
l+l+w+w=60
3w-6+3w-6+w+w=60
8w-12=60
8w=60+12=72
w=72/8
w=9
l=3w-6
l=27-6
l=21
∠A=6x−35 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 35, degrees, end color #11accd ∠ � = 3 � + 5 3 ∘ ∠B=3x+53 ∘
73 degrees is the equivalent meausure of m<A
Solving line geometryFrom the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:
m∠A + m∠B = 180
Given the following
∠A = 6x - 35
∠B = 3x + 53
Substitute the given parameters
6x - 35 + 3x + 53 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Determine the measure of <A
<A = 6x - 35
<A = 6(18) - 35
<A = 108 - 35
<A = 73 degrees
Hence the measure of angle A from the given diagram is 73 degrees
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Find the perimeter of the large triangle below
The perimeter of the triangle is equal to 28.7 using the trigonometric ratio
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
tan60 = q/4 {opposite/adjacent}
q = 4 × tan60 {cross multiplication}
q = 6.9282
sin60 = q/r {opposite/hypotenuse}
sin60 = 6.9282/r
r = 6.9282/sin60 {cross multiplication}
r = 8
sin45 = q/s {opposite/hypotenuse}
sin45 = 6.9282/s
s = 6.9282/sin45 {cross multiplication}
s = 9.8
cos45 = p/s {adjacent/hypotenuse}
cos45 = p/9.8
p = 6.9282 {cross multiplication}
perimeter of the triangle = 4 + p + s + r
perimeter of the triangle = 4 + 6.9282 + 9.8 + 8
perimeter of the triangle = 28.7282
Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.
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if TAN a =21/29 calculate the values of seca - coseca/seca+coseca
The values of sec a - cosec a/sec a+cosec a is 4/25.
Trigonometric ratios:The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
In a right-angled triangle,
Sin θ = Opposite Side /HypotenuseCos θ = Adjacent Side /HypotenuseTan θ = Opposite Side/Adjacent Side Sec θ = 1/cos θCosec θ = 1/sin θHere we have
tan A = 21/29
As we know Tan θ = Opposite side/Adjacent side
=> Opposite side = 21
=> Adjacent side = 29
In a right-angle triangle,
=> Hypotenuse² = Opposite side² + Adjacent side²
=> Hypotenuse² = 21² +29²
=> Hypotenuse² = 441 + 841
=> Hypotenuse² = (35.8)²
Cos a = Adjacent side /Hyopenuse = 29/ 35.8
Sin a = Opposite side/Hypotenuse = 21/35.8
The given expression can be solved as follows
=> [tex]\frac{seca - coseca}{seca+coseca } = \frac{ \frac{1}{cos a}-\frac{1}{sina} }{\frac{1}{cos a }+\frac{1}{sin a} }[/tex]
=> [tex]\frac{ \frac{sin a - cosa}{cos a sn a} }{\frac{sin a + cos a}{cos a sin a} }[/tex]
=> [tex]\frac{sin a - cosa}{cos a+ sin a}[/tex]
=> [tex]\frac{ \frac{21}{35.8} - \frac{29}{35.6} }{\frac{29}{35.8} + \frac{21}{35.8} }[/tex]
=> [tex]\frac{21- 29}{29+21}[/tex]
=> [tex]\frac{8}{50}[/tex]
=> [tex]\frac{4}{25}[/tex]
Therefore,
The values of sec a - cosec a/sec a+cosec a is 4/25.
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5.3A Find Two Numbers Whose Product and Sum is as Indicated
For product=6 and sum=7, the numbers or integers are 1 and 6.
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
now,
As given product=6 and sum=7
make factors for 6 i.e 1,2,3,6
from these choose the numbers whose sum=7
and they are 1,6.
Hence,
For product=6 and sum=7, the numbers are 1 and 6.
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Craig has a job waiting tables where he earns $3.35 per hour plus tips. Craig earned $73.96 in tips during his shift yesterday.
Q.If x represents the number of hours Craig worked yesterday, which of the following equations can be used to find the amount of money Craig earned yesterday?
A.y = 3.35x - 73.96
B.y = 73.96x + 3.35
C.y = 73.96x - 3.35
D.y = 3.35x + 73.96
Answer:
The correct answer is D. y = 3.35x + 73.96.
Step-by-step explanation:
D. y = 3.35x + 73.96
Solve d+5/-2<=-3/2 please help I will give brainly
Answer:
Step-by-step explanation:
inequality form
d≤ 1
Interval Notation:
(−∞,1]
In Iceland, the temperature drops when the sun goes down. The temperature at 5:00 is 5°C. By 9:00, the temperature had dropped 24°. If the temperature dropped at a constant rate, how much did it drop per hour?
If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).
The original price of a pair of running shoes was $95.00. They were on sale at 25% off, but the marked price was $73.25. Is this the correct price? Explain.
No, the marked price of $73.25 is not correct.
To calculate the sale price, we start by multiplying the original price by the discount percentage:
$95.00 * 0.25 = $23.75
This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:
$95.00 - $23.75 = $71.25
Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.
What is the doubling time for the investment? Round answer to 1 decimal place.
The amount of money in an investment is modeled by the function A(T)=650(1.0455)^T. The variable A represents the investment balance in dollars, and T the number of years.
The doubling time for the investment as required to be determined is; 15.58 years.
What is the value of the investments doubling time?It follows from the task content that the model function is;
A(T)=650 (1.0455) ^T
For doubling time;
2 = (1.0455)^T
ln (2) = T ln (1.0455)
T = ln 2 / ln (1.0455)
T = 15.58 years.
Ultimately, the doubling time of the investment as required is; 15.58 years.
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Write the set using set-builder notation
(9, 18, 27, 36, ...}
How do i do this
The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the value of A is
A = { 9 , 18 , 27 , 36 , ... }
The set A contains all the positive multiples of 9
So , let x be the set of natural numbers and the value of A is
A = { 9x | x ∈ N } , and
A = set of all x’s containing multiples of 9
Hence , the set builder notation is { 9x | x ∈ N }
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Evaluate the expression below when n = 9. If needed, answer as a fraction or a decimal.
n² + 6n ÷ 3
Answer:
Below
Step-by-step explanation:
Put '9' where 'n' is and compute
(9)^2 + 6(9) ÷ 3 =
81 + 54 ÷3 =
81 + 18 = 99
what is the value of Z in this figure Enter your answer in the box
Using the a pair of adjacent angles, we will see that:
Z° = 137°
What is the value of z on the diagram?When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.
Then here we can write a linear equation for z.
z + 43 = 180
Solving that for z, we will get:
z = 180 - 43
z = 137
That is the measure of the angle.
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1. Is Event 1 and Event 2 Mutually Exclusive of each other? Event 1: Pre- Schooler is a girl Event 2: Pre- Schooler prefers the color blue to the color pink Select one: a. No, A girl pre-schooler can prefer the color blue to the color pink. b. Yes, The gender of pre-schooler has no affect on color preference c. Yes, Girls prefer the color pink to the color blue 2. 70 preschoolers were asked whether they preferred blue or pink. 35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color. Assuming one of the pre-schoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
(9+w) (2w+3)=0
If there is more than one solution, please seperate with commas
The lengths of nails produced in a factory are normally distributed with a mean of 6.13
centimeters and a standard deviation of 0.06
centimeters. Find the two lengths that separate the top 7%
and the bottom 7%
. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
The two lengths that Bottom 7%: L= 6.04 cm
Top 7%: L= 6.22 cm
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
The level of variability within a particular data collection is effectively reflected in the standard deviation.
Mean length of the population (μ) = 6.13 cm
Standard deviation (σ) = 0.06 cm
The z-score for any given length 'X' is
Z = X - μ/σ
What we want to know is the length at the 7-th percentile and at the 93-rd percentile.
According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths
Z(Xb) = Xb - μ/σ
- 1.476 = Xb - 6.13/0.06
Xb = 6.04
z(Xt ) = Xt - μ/σ
1.476 = Xt - 6.13/0.06
Xt = 6.22
Bottom 7%: L= 6.04 cm.
Top 7%: L= 6.22 cm.
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An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
a. 4
b. 16
c. 8
d. 32
16 sample points (possible outcomes as to the classifications) exist.
What is the combination?
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
Here, we have
Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.
There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.
A total of (4)(4) = 16 sample points.
Hence, 16 sample points (possible outcomes as to the classifications) exist.
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In ADEF, J is the intersection of the three medians. If EI = 33, find JI.
D
Q
H
F
The value of JI in the given triangle is 11.
What is a triangle?A triangle is a polygon with three sides, vertices and angles.
Given that, in a triangle DEF, J is the intersection of the three medians.
EI = 33, we are asked to find the value of JI,
Since, all the median is intersecting at J, therefore, J is the centroid.
We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.
Therefore,
Let, EI = 3x,
JI = x,
Therefore, JI = 11
Hence, the value of JI in the given triangle is 11.
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The complete question is :
In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.
Figure is attached
