The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.
The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.
Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:
Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 4/(1 × 3/4) = 16/3 inches
Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 3/(1 × 3/4) = 4 inches
Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.
This can also be written as the mixed number 1 1/3 inches.
Learn more about the volume here:
brainly.com/question/23118276
#SPJ1
questions 1, 2 and 3 please!
will give brainliest to whoever answers
80 points
Answer:
a) [tex]f(x) = x + 3[/tex]
b) [tex]f(x) = -x - 5[/tex]
c) [tex]f(x) = 2x + 6[/tex]
Step-by-step explanation:
To determine the equation of a straight line, we need two things:
1. two known points (coordinates) on the line, used to calculate the gradient
2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)
Then we can use the equation:
[tex]\boxed {f(x) = ax + q}[/tex]
where a is the gradient and q is the y-intercept, to determine the equation of the line.
a) known points: (0, 3), (-4, -1)
y-intercept: 3
gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]
⇒ [tex]\bf 1[/tex]
∴ a = 1 , q = 3
∴ equation:
[tex]{f(x) = ax + q}[/tex]
[tex]f(x) = 1x + 3[/tex]
⇒ [tex]\bf f(x) = x + 3[/tex]
b) known points: (-7, 2) , (0, -5)
y-intercept = -5
gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]
⇒ [tex]\bf -1[/tex]
∴ equation:
[tex]f(x) = -1x + (-5)[/tex]
⇒ [tex]\bf f(x) = -x - 5[/tex]
c) known points: (-3, 0), (0, 6)
y-intercept = 6
gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]
⇒ [tex]\bf 2[/tex]
∴ equation:
[tex]\bf f(x) = 2x + 6[/tex]
Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 11 lb stretches a certain spring 9 in., how much will a force of 22 lb stretch the spring?
Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The measures are direct proportional, hence the rule of three is:
11 lb - 9 inches
22 lb - n inches
Applying cross multiplication:
11n = 9 x 22
n = 9 x 2
n = 18 inches.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
What does the acronym EDI stand for ? a ) Electronic data interchange b ) Electronic duty interruption c ) Estimated duration indication Extreme data interchange d )
electronic data interchange
Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.
Using simple interest, it is found that the APR is of 4.472%.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.The parameters are given as follows:
A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.
Hence the APR is found as follows:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]3067.08 = 3000(1 + 0.5r)[/tex]
[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]
1 + 0.5r = 1.02236
r = (1.02236 - 1)/0.5
r = 0.04472.
More can be learned about simple interest at https://brainly.com/question/25296782
#SPJ1
Josue has a coin collection. He keeps 11 of the coins in his box, which is 5% of the collection. How many total coins are in his collection?
Answer:
220
Step-by-step explanation :
11 = 5%
100 ÷ 5 = 20
11 × 20 = 220
0.05 × 220 = 11 ✓
0.05 = decimal multiplier of 5%
write the explicit formula for this geometric sequence.
81,27,9,3, …
Find the common ratio, r.
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.
The geometric sequence 81, 27, 9, 3, … has common ratio:
r = 27/81 = 1/3
The explicit formula for this geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
if the area of the figure below is 400m. find x
Answer:
it's answer came 20000o
The sum of two numbers is 43 . The smaller number is 9 less than the larger number. What are the numbers?
Answer:
17 & 26
Step-by-step explanation:
The equation
[tex]x+(x+9)=43\\2x+9=43[/tex]
[tex]2x=43-9\\2x=34[/tex]
[tex]x=34/2=17[/tex]
One number is 17
The other number is:
[tex]x+9=17+9=26[/tex]
Hope this helps
there were 936,795 bankruptcy filings in 2018. If there were 310,061 chapter 13 filings, what percent were not chapter 13
66.90% of the total bankruptcy fillings are not chapter 13 fillings.
What is bankruptcy?
This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.
In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings
fillings that were not chapter 13=936,795-310,061
fillings that were not chapter 13=626,734
fillings that were not chapter 13 as % of total fillings=626,734/936,795
fillings that were not chapter 13 as % of total fillings=66.90%
Learn more on bankruptcy on:https://brainly.com/question/4418659
#SPJ1
Which statement is true about the slope of the graphed line?
A graph is a line that extends from second quadrant to first quadrant with y-intercept at 4.
A.
The slope is negative.
B.
The slope is positive.
C.
The slope is zero.
D.
The slope is undefined.
Answer:
c
Step-by-step explanation:
because I had a test on these
centered at the origin given its...
Give the equation of the circle centered at the origin and passing through the point (0, -5).
Step-by-step explanation:
the equation of a circle centered at the origin is
x² + y² = r²
r being the radius (the distance of the center to every point on the circle's arc).
so, we get a point on the arc : (0, -5).
what is its distance to the origin ?
the origin is (0, 0).
we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.
that means there is no distance between them in x direction.
the only distance is in y direction : 0 to -5.
a distance is always positive (no matter in what direction).
so, the distance from 0 to -5 is : 5 units.
that means r = 5.
and our equation is
x² + y² = 5² = 25
How many words can be formed by using all the letters of the word AWILLO, if the two L's are to be separated?
There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
The experiment is not a binomial experiment.
What is a binomial experiment?
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.
The conditions for a binomial experiment include:
1. Each trial should be classified either as a success or a failure.
2. There are a fixed number of observations
3. The trials are independent.
4. The number of trials are fixed.
To learn more about binomial experiments, please check: https://brainly.com/question/25868945
#SPJ1
101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Distribute the summation over the sum.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]
Now plug in the known sums and simplify.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]
choose the correct option that explains what steps were followed to obtain the system of equations below x+6y = 5
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
System A:
x + 6y = 5 and; 3x - 7y = -35
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.
System B:
x + 6y = 5 and; - 25y = -50
The solution of system B will be the same as the solution of system A.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Question 1 of 10
What is the slope of the line that contains the points (-2, 5) and (6,-3)?
OA. 8
OB. 1
O C. -1
OD. -8
Answer:
slope is -1
Step-by-step explanation:
Slope of the line is changes in y over changes in x. It can also be referred as rise over run.
We can express mathematically as:
[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m is slope.
Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:
[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]
Therefore, the slope is -1
Suppose we want to choose 2 colors, without replacement from 3 colors red blue and green how many ways can this be done in the order of the choice is relevant and not relevant
The two colors can be chosen in 3 different ways.
In how many ways can we choose two colors?
If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.
Replacing that we get:
[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]
The two colors can be chosen in 3 different ways.
If you want to learn more about combinations:
https://brainly.com/question/11732255
#SPJ1
For what value of x is the rational expression below undefined x-4/3x2-75
The given expression is undefined when x = 5 OR x = -5
Undefined expressionFrom the question, we are to determine the value of x for which the given expression is undefined
The given expression is
x-4/3x²-75
An expression is undefined when the denominator equals zero
Thus, the expression is undefined when
3x² - 75 = 0
Now, we will determine the values of x in the equation above
3x² - 75 = 0
3x² = 75
x² = 75/3
x² = 25
x = ±√25
x = ±5
Hence, the given expression is undefined when x = 5 OR x = -5
Learn more on Undefined expression here: https://brainly.com/question/19815575
#SPJ1
I run 3 miles in 20 minutes. What was my average speed in miles per hour?
9 and 1/9 subtracted by 1 and 4/5
Answer:
7 14/45
Step-by-step explanation:
9 1/9 - 1 4/5
82/9 - 9/5
410/45 - 81/45
329/45
7 14/45
Answer:
●7.31
please mark as brainliest
A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality 90 greater-than 2.50 (x + 5) to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?
Answer:
Step-by-step explanation:
x is the number of students
(x+5) is the number of students and chaperons
$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have
2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)
The inequality "90 greater-than 2.50 (x + 5) "
90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign
90 ≥ 2.50(x+5)
Assume that the random variable X is normally distributed, with mean and standard deviation . Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.
Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:
[tex]P(X \leq 40) = 0.1587[/tex]
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation of the distribution are given, respectively, by:
[tex]\mu = 51, \sigma = 11[/tex]
The probability that x is of at most 40 is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 51}{11}[/tex]
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the probability is:
[tex]P(X \leq 40) = 0.1587[/tex]
Which is the part to the left of X = 40 of the distribution, hence option B is correct.
More can be learned about the normal distribution at https://brainly.com/question/28135235
#SPJ1
I’m confused in the exponential
These are the laws of indices. You just have to memorise it, sorry : (
Hope it helps : )
If R={(1,2),(2,3),(3,9),(4,5)} find R-1
Answer:
[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}
Step-by-step explanation:
Solution Given:
To find the inverse we need to exchange Domain to Range and vice-versa.
so
[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}
please help with this question
The value of angle TUS based on the information given about the circle will be 49°.
What is a circle?It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Here, the value of TUS will be:
= 1/2 × TRS
= 1/2 × 98°
= 49°
In conclusion, the correct option is 49°.
Learn more about circle on:
https://brainly.com/question/4293362
#SPJ1
Complete question:
Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?
Solve for x: 4(x + 2) = 3(x - 2) (1 point)
0-2
O-4
O-10
O -14
Answer:
its -14
Step-by-step explanation:
What fraction with a denominator of 32 is equal to 1/2?
Answer:
[tex]\frac{16}{32}[/tex]
Step-by-step explanation:
given
[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )
= [tex]\frac{16}{32}[/tex]
Remove all perfect squares from inside the square roo
√28
Answer:
√2² cannot be answer yesah
suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks
The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
The question has to do with definite integrals
What are definite integrals?Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.
Given that
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex] and also [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex] and we require [tex]\int\limits^{10}_5 {g(x)} \, dx[/tex]For any integral [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
Since
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex]and [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex]Substituting the values of the variables into the equation, we have
[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
Learn more about definite integrals here:
https://brainly.com/question/24353968
#SPJ1