A disadvantage of debt consolidation is you can pay more money in the long term.
What is debt consolidation?
Debt consolidation is when a person takes out a new loan in order to pay off an existing loan. Debt consolidation increases the money you pay in the long term because you would still have to pay for the new debt incurred.
To learn more about debt consolidation, please check: https://brainly.com/question/14309069
#SPJ1
Easy! 40 PTS!!! Log Functions
Answer:
C
Step-by-step explanation:
When x is negative 1/2 ^x becomes 1 / ( 1/2 ^x) meaning it is quite large as x becomes more negative
when x = 0 the value is 1
as x increases from 0 to + inf the value becomes smaller...but never negative
the only graph that fits is C
i am not able to solve this problem
Answer:
C
Step-by-step explanation:
you know the drill
The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours. How many total miles did the Ramos family drive?
ASAP
Anyone is here
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours -> They drove a total of 55 x 3 = 165 miles.
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours -> They drove a total of 45 x 2 = 90 miles.
So, the total amount of miles the Ramos family drove is 165 + 90 = 255 miles.
Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours.
[tex]\longrightarrow \tt{55*3=165}[/tex]
After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.
[tex] \longrightarrow \tt{45*2=90}[/tex]
Total miles the Ramos family drive
[tex] \longrightarrow \tt{165+90=255}[/tex]
[tex]answer : \pink{255} \: \tt{miles}[/tex]
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Kindly help!
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Radius of first sphere [tex]\sf r_{1}[/tex] = 6cm.
★ Radius of second sphere [tex]\sf r_{2}[/tex] = 8cm.
★ Radius of third sphere [tex]\sf r_{3}[/tex] = 10cm.
[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The radius of the resulting sphere formed.
[tex] {\large{\textsf{\textbf{\underline{\underline{Formula \: used :}}}}}}[/tex]
[tex]\star \: \tt Volume \: of \: sphere = {\underline{\boxed{\sf{\red{ \dfrac{ 4}{3}\pi {r}^{3} }}}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}[/tex]
★ As, three spheres are melted to from one new sphere. Therefore, volume of three old sphere is equal to volume of new sphere.
i.e, Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
The radius of resulting sphere be [tex]R[/tex]
According to the question,
• Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(r_{1})}^{3} + \dfrac{4}{3} \pi {(r_{2})}^{3} + \dfrac{4}{3} \pi {(r_{3})}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
• here
☆[tex]\: \sf r_{1}[/tex] = 6cm
☆[tex]\: \sf r_{2}[/tex] = 8cm
☆[tex]\: \sf r_{3}[/tex] = 10cm
Putting the values,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(6)}^{3} + \dfrac{4}{3} \pi {(8)}^{3} + \dfrac{4}{3} \pi {(10)}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
Taking " [tex]\dfrac{4}{3} \pi [/tex]" common,
[tex] \longrightarrow \sf \dfrac{4}{3} \pi \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \dfrac{4}{3} \pi {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \cancel{ \dfrac{4}{3} \pi} \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \cancel{ \dfrac{4}{3} \pi } {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \bigg[ 216 +512 + 1000 \bigg] = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf 1728 = {(R)}^{3} [/tex]
[tex]\longrightarrow \sf \sqrt[3]{1728} = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ 12 \times 12 \times 12 } = R[/tex]
[tex]\longrightarrow \sf \sqrt[3]{ {(12)}^{3} } = R[/tex]
[tex]\longrightarrow \sf R = \red{12 \: cm} [/tex]
Therefore,
Radius of the resulting sphere is 12cm.
[tex]{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}[/tex]
★ Figure in attachment.
[tex]{\underline{\rule{290pt}{2pt}}}[/tex]
5x-4y=19
x+2=8
Solve simultaneous equation
Answer:
x = 6, y = 5
Step-by-step explanation:
5x - 4y = 19 -------> equation 1
x + 2 = 8 --------> equation 2
Step 1 : Subtract 2 on both sides in equation 2.
x + 2 - 2 = 8 - 2
x = 6
Step 2 : Substitute the value of x is equation 1.
5 ( 6 ) - 4y = 19
( 5 * 6 ) - 4y = 19
30 - 4y = 10
Step 3 : Subtract 30 on both sides.
30 - 30 - 4y = 10 - 30
- 4y = - 20
Step 4 : Multiply - 1 on both sides.
- 1 * - 4y = - 1 * - 20
4y = 20
Step 5 : Divide 4 on both sides.
4y / 4 = 20 / 4
y = 5
Hence,
x = 6
y = 5
Answer:
x = 5, y = 3/2.
Step-by-step explanation:
5x-4y=19
x+2y =8 Multiply this by 2:
2x + 4y = 16 Adding this to first equation 1:
7x = 35
x = 5
So
5 + 2y = 8
2y = 3
y = 3/2.
What is the diameter of this circle if the circumference is 30 inches?
Answer:
d≈9.55
Step-by-step explanation:
the answer is 9.55 inches
Answer:
diameter = 9.55 in
Step-by-step explanation:
Circumference = pi x diameter so re-arrange
circumference / pi = diameter
30 / pi = diameter
9.55 in = diameter
(y^3-2)(y^2+11) what is the answer
Answer:
[tex]y^{5}[/tex] + 11y³ - 2y² - 22
Step-by-step explanation:
(y³ - 2)(y² + 11)
each term in the second factor is multiplied by each term in the first factor.
y³(y² + 11) - 2(y² + 11) ← distribute both parenthesis
= [tex]y^{5}[/tex] + 11y³ - 2y² - 22
Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Considering the given probability distributions, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.The sum of all probabilities is of 1.In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.
More can be learned about probability distributions at brainly.com/question/23670007
#SPJ1
Answer:
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Step-by-step explanation:
The answer above is correct.
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50. The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5. If she has a total of 30 notes, how many notes of each denomination she has.
Answer:
Given that,
Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.
The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.
She has a total of 30 notes with her.
Let assume that
Number of Rs 10 notes be 2x
Number of Rs 20 notes be 5x
Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x
So,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
Now,
Amount in form of Rs 10 = 10 × 2x = Rs 20x
Amount in form of Rs 20 = 20 × 5x = Rs 100x
Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x
Now, According to statement
[tex]\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}[/tex]
[tex]\sf \: \implies x = 2 [/tex]
Hence,
[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]
━━━━━━━━━━━━━━━━━━━━━Given the following graph of a point on the polar plane, name another set of coordinates that could also represent this point using a
positive "value and a negative "O" value, where -360 ≤ 0 ≤ 0. State your answer in the form: (r,0) with "O" in degrees without the
degree symbol.
Answer:
(r,0)
Step-by-step explanation:
Identify the axis of symmetry the function graphed below.
Answer: A. X = -1
Step-by-step explanation:
An axis of symmetry is the line that divides the object into two equal halves, creating a mirror-like reflection. Only at x = -1 will that occur.
A coordinate grid showing Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15).
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. What is the system of equations representing these costs?
y = 5.5x and y = 7.5x + 10
y = 7.5x and y = 5.5x
y = 7.5x and y = 5.5x + 10
y = 7.5x + 10 and y = 5.5x + 10
The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10
How to find the equation of a line?The slope of the first line is;
m = (y2 - y1)/(x2 - x1)
m = (32 - 10)/(4 - 0)
m = 5.5
Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10
The slope of the second line is;
m = (y2 - y1)/(x2 - x1)
m = (15 - 0)/(2 - 0)
m = 7.5
Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x
Thus, the system of equations representing these costs are;
y = 7.5x and y = 5.5x + 10
Read more about Equation of a line at; https://brainly.com/question/13763238
#SPJ1
Answer:
y = 7.5x and y = 5.5x + 10
Step-by-step explanation:
Solve the following equation:
(d - 3) tan 37°
17
Give your answer to 1 d.p.
-
Answer: 25.6
Step-by-step explanation:
[tex](d-3) \tan 37^{\circ}=17\\\\d-7=\frac{17}{\tan 37^{\circ}}\\\\d=\frac{17}{\tan 37^{\circ}}+3 \approx \boxed{25.6}[/tex]
which of the following statements must be true abut this diagram. check all that apply
The options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
From the figure,
The interior angle of a triangle is w
w > x (true)
w > y (true)
x + y = w (sum of the two interior angles is equal to the exterior angle)
Thus, the options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.
Learn more about the angle here:
brainly.com/question/7116550
#SPJ1
Help fast. i really need help fast
Answer: 80 miles
Step-by-step explanation:
- 400/5 = 80
- so 80 is 1/5 of 400
hope this helps :)
Answer:
80 miles
Step-by-step explanation:
The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles
If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.
Answer:
a = 2
Step-by-step explanation:
given x = - 1 is a zero then f(- 1) = 0 , that is
a(- 1)³ - (- 1)² - 1 + 4 = 0
- a - 1 - 1 + 4 = 0
- a + 2 = 0 ( subtract 2 from both sides )
- a = - 2 ( multiply both sides by - 1 )
a = 2
[tex] \bf \huge x {}^{2} + 5 = 6[/tex]
solve for x :
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \textsf{Song recommendations \:? }~ [/tex]
Given :
x² + 5 = 6Subtract 5 from each side :
x² + 5 - 5 = 6 - 5x² = 1Take the root on each side :
√x² = √1x = ±1Hence, the values of x are :
[tex]\fbox {x = 1}[/tex][tex]\fbox {x = -1}[/tex][tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]
How many 50c make up $200
Answer:
40. 50c goes into 200 40 times
A book seller gains 30% on the cost price by selling a book for $130.Calculate the cost price of the book.
Answer:
Let the cost price be x
Selling price, S.P. = 130Gain % = 30%[tex]\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}[/tex]
[tex]\rm{C.P. = \dfrac{130 \times 100}{100+30}}[/tex]
[tex]\rm{ C.P. = \dfrac{130}{30} }[/tex]
[tex]\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}[/tex]
Cai invests £2500 in an account that pays 3.55% simple interest interest per year. He takes out his money after 2.75years. what is the value of the investment when he takes out the investment
Answer:
So now,
you know the formula for simple interest is P×R×T divided by a hundred?
So 2500 times 3.55 times 2.75 divided by 100
Please help I’ve tried to answer this 3 times and I keep getting it wrong
Answer:
[tex] \boxed{\bf A. \: x - 2}[/tex]
Step-by-step explanation:
[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]
First, we need to factor the expressions that are not already factored.
[tex] \sf ( x - 2) ( x + 4) / x + 4 [/tex]Now, let's Cancel out x+4 in both numerator and denominator.
[tex] \sf x - 2 [/tex]----------------------------
What is the slope of each of these three graphs?
[5] No slope (or a slope of 0)
There is no incline or decline to the line, so there is no slope.
[6] 1
We can use "rise over run" since we have clear points on the graph. See attached.
[7] Undefined slope
This slope of this line is undefined. The formula for slope is [tex]\frac{\text{change in y}}{\text{change in x}}[/tex] which becomes [tex]\frac{0}{0}[/tex] in a case like this. You cannot divide by 0, giving a slope of undefined.
If the set u = {all positive integers} and set a = {x|x ∈ u and x is an odd positive integer}, which describes the complement of set a, ac?
A = {x|x ∈ U and is an even positive integer}
The universal set(U) consists of only positive integers.
Given, A = {x|x ∈ U and x is an odd positive integer}.
That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.
refers to the complement of A. It means that it will contain all those elements that belong to U but does not belong to A.
All the positive odd integer is made up of two types of number ,i.e, positive and negative number.
So,this set will contain all the element belonging to U and should be an even positive integer.
Therefore,Ac = {x|x ∈ U and is an even positive integer}.
Learn more about Sets:
https://brainly.com/question/2166579
#SPJ4
Answer:D:Ac = {x|x ∈ U and is an even positive integer}
Step-by-step explanation:
edge 2022
A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is
The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
Sample size (n) = 16.
Sample mean = 2.8 minutes.
Sample standard deviation (σ) = 1.2 minutes.
Confidence interval given = 95%.
The degree of freedom (df) can be calculated as n - 1.
df = n - 1 = 16 - 1 = 15.
Since, the level of confidence is 95%, the level of significance α = 1 - 0.95 = 0.05.
From the T-Distribution table, we take the value at critical value α/2 with the degree of freedom 15.
[tex]t_{\frac{\alpha }{2} ,15}[/tex] = 2.131.
Now, the margin of error can be shown as follows:
[tex]E = t_{\frac{\alpha }{2} ,15} * \frac{\sigma}{\sqrt{n} } \\\Rightarrow E = 2.131 * \frac{1.2}{\sqrt{16} }\\ \Rightarrow E = 0.6393[/tex]
The width at the confidence interval of 95%, is twice the margin of error, that is:
Width = 2*E = 2*0.6393 = 1.2786.
Thus, the width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.
Learn more about the width of distribution at
https://brainly.com/question/19338886
#SPJ4
In the following exercises, multiply the binomials. Use any method.
249. (6p + 5)(p + 1)
Answer:
Hence the expression [tex]$$(6p+5)(p+1)=6p^2+11p+5$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (6p+5)(p+1).We have to multiply the given expression.Multiply the (6p+5) by 1 , multiply the (6p+5) by p then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$[/tex]
Given that
5,6,-2,4,8,1,1,1,1,1
• find the mean
mode
median
Answer:
mean: 2.6, mode: 1, median: 1
Step-by-step explanation:
The mean is essentially the average of the data set which can be defined as: [tex]\frac{\text{sum of data set}}{\text{amount of data in data set}}[/tex]. So adding all the values together you get: [tex]26[/tex]. and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: [tex]\frac{26}{10} = 2.6[/tex] which is the mean
To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode
To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1
what’s the sun of -6 4/5 and 6 4/5
Answer:
the answer is 0.
Step-by-step explanation:
When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]
[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]
[tex]\mathsf{= 0}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
determine intervals when the graph is concave up or concave down
The graph is concave has two curved part as follows;
The graph is concave up between;(0, 1), and (1, 0)The graph is concave down between; (0, 1), and (-a, 2)How can the direction of concavity be found?The direction the concave part of the graph faces is given as follows;
The graph is concave up when the concave part faces up
It is concave down when the concave part faces down
From the given diagram, we have;
The graph is concave up between;
(0, 1), and (1, 0)
The graph is concave down between; (0, 1), and (-a, 2)
Where a is in the range; 1 < a < 2
Learn more about graphs here:https://brainly.com/question/17136458
#SPJ1
Geometry question I’m confused with this help
Answer: ∠PQR = 130°
Step-by-step explanation:
The word bisects means that angle PQS and SQR are equal to each other.
3x + 5 = 2x + 25
3x = 20
x = 20
Now, we will plug this value back in and solve for angle PQR. There are three ways we could do this.
[1]
(3x + 5) + (2x + 25)
(3(20) + 5) + (2(20) + 25)
(60 + 5) + (40 + 25)
(65) + (65)
130 degrees
[2]
(3x + 5) * 2
(3(20) + 5) * 2
(65) * 2
130 degrees
[3]
(2x + 25) * 2
(2(20) + 25) * 2
(65) * 2
130 degrees
Triangle not drawn to scale
Given: m&A=40°,m&B=88°,a=15cm. Then b
= _?__cm to the nearest hundredth
Answer:
b = 23.3
Step-by-step explanation:
First, we need to determine whether this is a right or non-right triangle.
We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:
[tex]180-(40+88)=180-128=52[/tex]
The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.
Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3[/tex]