Question:
Fill in the blank.
23 x 6 = (20 + 3) * 6
23 x 6 = _ + (3x6)
Options
20 * 6
20 * 3
20 * 5
Answer:
20 * 6
Step-by-step explanation:
Given
Expression 1: 23 * 6 = (20 + 3) * 6
Expression 2: 23 * 6 = __ + (3 * 6)
Required
Fill in the blank
From Expression 1
23 * 6 = (20 + 3)*6
Using Distributive Property; The expression becomes
23 * 6 = 20 * 6 + 3 * 6
23 * 6 = (20 * 6) + (3 * 6)
By Comparing this with expression 2
23 * 6 = __ + (3 * 6)
The blank position is occupied by 20 * 6.
Hence, the correct option that fills the missing blank correctly is 20 * 6
The correct option that fills the missing blank correctly is 20 * 6.
The blank position is occupied by 20 * 6.
Here, we have,
Given
Expression 1: 23 * 6 = (20 + 3) * 6
Expression 2: 23 * 6 = __ + (3 * 6)
Required
Fill in the blank
From Expression 1
23 * 6 = (20 + 3)*6
Using Distributive Property;
The expression becomes
23 * 6 = 20 * 6 + 3 * 6
23 * 6 = (20 * 6) + (3 * 6)
By Comparing this with expression 2
23 * 6 = __ + (3 * 6)
The blank position is occupied by 20 * 6.
Hence, the correct option that fills the missing blank correctly is 20 * 6.
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complete Question:
Fill in the blank.
23 x 6 = (20 + 3) * 6
23 x 6 = _ + (3x6)
Options
20 * 6
20 * 3
20 * 5
Find the slope of the line that contains the points named.
R(O, 4), S(5,0)
-4/5
4/5
-5/4
Answer:
[tex] - \frac{4}{5} [/tex]
Step-by-step explanation:
Line is passing through the points R (0, 4), S (5, 0)
[tex]Slope \: of \: RS \\ = \frac{4 - 0}{0 - 5} \\ \\ = \frac{4}{ - 5} \\ \\ = - \frac{4}{5} [/tex]
Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink has 45% sugar. Each can has 250 milliliters of soda. What is the sugar concentration of the mixed soft drink?
Answer:
Sugar concentration of the mixed soft drink will be 32.5%.
Step-by-step explanation:
Sugar concentration of first drink = 20%
Volume of first soda = 250 ml
Sugar in first soda = 20% of 250 ...... (1)
Sugar concentration of second drink = 45%
Volume of second soda = 250 ml
Sugar in second soda = 45% of 250 ...... (2)
Let [tex]x\%[/tex] be the sugar concentration in resultant mixture.
Volume of mixture = 250 + 250 = 500 ml
Sugar in mixture = [tex]x\%[/tex] of 500 ml ...... (3)
Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):
20% of 250 + 45% of 250 = [tex]x\%[/tex] of 500
[tex]\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%[/tex]
Hence, Sugar concentration of the mixed soft drink will be 32.5%.
What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?
Answer:
12 and -12
Step-by-step explanation:
12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12
Brainliest to best answer!
Understanding proofs can be challenging for many students. What advice would you
give to a student struggling with these concepts?
Answer:
take your time and always ask for help when needed
Step-by-step explanation:
A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Answer:
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.28[/tex]
So
[tex]\mu = E(X) = np = 100*0.28 = 28[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.28*0.72} = 4.49[/tex]
What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Using continuity correction, this is [tex]P(20 - 0.5 \leq X \leq 30 + 0.5) = P(19.5 \leq X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 19.5.
X = 30.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 28}{4.49}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.7123.
X = 19.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 28}{4.49}[/tex]
[tex]Z = -1.89[/tex]
[tex]Z = -1.89[/tex] has a pvalue of 0.0294
0.7123 - 0.0294 = 0.6829
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Express the ratio 16:9 as a ratio to 1.
Answer:
(16/9):1
Step-by-step explanation:
Find the measure of an angle whose supplement measures five times its measure.
The angle measure ___ degrees.
Answer:
30°
Step-by-step explanation:
supplementary angles are two sets of angles whose sum form 180°
According to the problem, one set equals 5 times the other.
Let the other be x,
It means it's compliment is 5x;
It means therefore that ;
x + 5x = 180°
6x = 180°;
x = 180°/ 6 = 30°;
Therefore the angle measures 30° and it's supplement 150°.
Bilal's favorite colors are red and green.
He has 1 red shirt, 1 green shirt, 1 red hat, 1 green scarf, 1 red pair of pants, and
1 green pair of pants.
Bilal selects one of these garments at random. Let A be the event that he selects a green garment and let
B be the event that he chooses a scarf.
Answer:
P(A∪B) = 1/3
Step-by-step explanation:
Red Garments = 1 red shirt + 1 red hat + 1 red pairs of pants
Total Red Garments = 3
Green Garments = 1 green shirt + 1 green scarf + 1 green pairs of pants
Total Green Garments = 3
The total number of garments = Total Red Garments + Total Green Garments:
3 + 3 = 6
Let A be the event that he selects a green garment
P(A) = Number of required outcomes/Total number of possible outcomes
P(A) = 3/6
Let B be the event that he chooses a scarf
P(B) = 1/6
The objective here is to determine P(A or B) = P(A∪B)
Using the probability set notation theory:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = P(A) - P(B)
= 3/6-1/6
= 2/6
P(A∪B) = 1/2 + 1/6 - 2/6
P(A∪B) = 2/6
P(A∪B) = 1/3
Answer:
in the khan academy answer is both A and B are dependent on each other.
I need help with this question
Answer:
A 120 deg
Step-by-step explanation:
The sum of the measures of all angles of a circle is 360 deg.
m<HML + m<LMK + m<KMJ + m<JMH = 360 deg
m<HML = 80 deg
m<LMK = 125 deg
m<KMJ = 35 deg since it's the same measure as the measure of arc KJ.
m<HML + m<LMK + m<KMJ + m<JMH = 360 deg
Now we substitute the values we know.
m<80 deg + m<125 deg + 35 deg + m<JMH = 360 deg
240 deg + m<JMH = 360 deg
m<JMH = 120
Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.
Answer:
Speed of a= 21 miles/hr
r = Speed of b= 7 miles/hr
Speed of a = 3r
Step-by-step explanation:
The cyclist are 112 miles apart
Time traveled by two = 4 hours
Speed of a = 3 * speed of b
If a cylcles 3 times More than b, then a will cover 3*distance of b
But speed = distance/time
Time = 4hours
Total distance=112
a = 3b
3b + b = 112
4b = 112
b = 112/4
b = 28 miles
a = 3b
a = 3*28
a = 84 Miles
They bought traveled 4 hours
Speed of a = 84miles/4 hours
Speed of a= 21 miles/hr
Speed of b = 28miles/4 hours
Speed of b = 7 miles/hr
4. In an electrical circuit it is known that the voltage V varies as the current I
(ie. that V is directly proportional to 1). It is also known that V = 36
when I = 8.
a Find a formula for V in terms of I.
b Find V when I = 14.
с Find / when V = 27.
Step-by-step explanation:
V∝I
V=kI
36=k*8
k=36/8
k=4.5
a. V=4.5I
b. V=4.5*14
V= 63
c. 27=4.5I
I=27/4.5
I= 6
I've been stuck on this for a little while now. Could anybody help?
Answer:
7
Step-by-step explanation:
The arrows on the diagonal lines mean those lines are parallel. That means the triangles are similar, so corresponding sides have the same ratio.
There are many ways we can write the proportion expressing that fact. It is convenient to do so with the variable in the numerator:
(3x -6)/12 = 10/8
Multiplying by 4, we have ...
x -2 = 5
x = 7 . . . . . . add 2
In Don Javier's milking, milk is collected in two containers, one with a 300-liter capacity and one with 180 liters, if they are filled with 15 and 20-liter jugs. Which of the pitchers exactly fill the containers without milk being left over or missing?
Answer:
Both Pitchers
Step-by-step explanation:
First, we determine how many of each pitcher it would take to fill the 300 liter and 180 liter containers.
300÷15=20 of the 15 liter pitcher
300÷20=15 of the 20 liter pitcher
Similarly
180÷15=12 of the 15 liter pitcher.
180÷20=9 of the 20 liter pitcher.
The two pitchers gives a whole number when their volumes divide the volumes of the containers.
Therefore, the two pitchers exactly fill the containers without milk being left over.
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A. g(x) = f(x - 5)
B. g(x) = f(x) - 2
C. g(x) = f(x + 2)
D. g(x) = f(x) - 5
Answer:
D. g(x) = f(x) - 5
Step-by-step explanation:
To move the intercept to -2, one needs to translate the function down by 5 or left by 5. The first translation (down 5) would result in ...
g(x) = f(x) - 5 . . . . . . matches choice D
The second translation (left 5) would result in ...
g(x) = f(x+5) . . . . doesn't match any available choice
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
A middle school band is selling candy bars and nuts to raise money for a field trip. Each candy bar, b, costs $1.50 and each box of nuts, n, costs $4.00. If they raised $418, what expression shows the portion that came from candy bar sales?
Answer:
1.5b = 418 - 4n (all in dollars)
Step-by-step explanation:
Let b represent the number of candy bars sold and n the number of box of nuts sold.
Given that each;
Candy bar costs $1.50
box of nut $4.00
Amount raised from candy bars = $1.50 × b
Amount raised from box of nut = $4.00 × n
Total amount raised = $418
The equation for the total amount raised is;
1.50 × b + 4.00 × n = 418
1.5b + 4n = 418
The portion that came from candy bars is;
Making 1.5b the subject of formula;
1.5b = 418 - 4n
Which phrase represents the algebraic expression 3d+7?
Answer:
3 multiplied by a variable d and add seven to it
Step-by-step explanation:
3 multiplied by a variable d and add seven to it.
7x-3y=4 2x-y=1 the solution to the system of equations is
Answer:
x = 1 and y = 1
Step-by-step explanation:
7(1) minus 3(1) = 4
and 2(1) minus 1 = 1
just try and guess a number and try to solve the problem with that number, if it isn't the answer then repeat.
Answer: Use the app: photomath
Step-by-step explanation:
Plot the image of point A under a reflection across the
y-axis.
Answer:
(-2,5)
Step-by-step explanation:
A reflection across the y axis (x,y)→(−x,y)
Point A is at (2,5) so it becomes (-2,5)
Answer:
(-2,5)
a reflection across the y axis causes for it to basically be reversed along the y axis. meaning if it is at (2,5) then it will be (-2,5)
Find the 17th term of the arithmetic sequence.
-6, 3, 12, 21, ...
The 17th term is
Answer:
nth term = dn + (a - d) Where d is the difference between the terms, a is the first term and n is the term number.
Step-by-step explanation:
9*17 + (-6- 9)= 138
First find the common difference.
This can be found by subtracting the second term minus the
first term which in this case us 3 - (-6) or 3 + (+6) which is 9.
So we add 9 to reach the next term in this sequence.
Since this sequence isn't too long, continuing adding 9
until you reach the 17th term in this arithmetic sequence.
-6 ⇒ 1st term
3 ⇒ 2nd term
12 ⇒ 3rd term
21 ⇒ 4th term
30 ⇒ 5th term
39 ⇒ 6th term
48 ⇒ 7th term
57 ⇒ 8th term
66 ⇒ 9th term
75 ⇒ 10th term
84 ⇒ 11th term
93 ⇒ 12th term
102 ⇒ 13th term
111 ⇒ 14th term
120 ⇒ 15th term
129 ⇒ 16th term
138 ⇒ 17th term
By manually doing this, we found that our 17th term is 138.
Find the product or type
"impossible".
3 -5 4 2
Answer:
The product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex] is [tex]\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex].
Step-by-step explanation:
A matrix is a rectangular arrangement of numbers into rows and columns.
Matrix multiplication refers to the product of two matrices.
The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one.
To find the product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex]
[tex]\mathrm{Multiply\:the\:rows\:of\:the\:first\:matrix\:by\:the\:columns\:of\:the\:second\:matrix}\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=3\cdot \:4+\left(-5\right)\left(-4\right)\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=3\cdot \:2+\left(-5\right)\cdot \:2\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=1\cdot \:4+7\left(-4\right)\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=1\cdot \:2+7\cdot \:2[/tex]
[tex]\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}3\cdot \:4+\left(-5\right)\left(-4\right)&3\cdot \:2+\left(-5\right)\cdot \:2\\ 1\cdot \:4+7\left(-4\right)&1\cdot \:2+7\cdot \:2\end{pmatrix}[/tex]
[tex]\mathrm{Simplify\:each\:element}\\\\\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex]
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
1. Calculate and print the mean points scored by your team during the years you picked.
2. Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it.
3. Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
4. Calculate and print the test statistic rounded to two decimal places.
5. Calculate and print the P-value rounded to four decimal places.
Answer:
1. M=108
2. μ=110
3. In the explanation.
4. Test statistic t = -1.05
5. P-value = 0.1597
Step-by-step explanation:
The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.
We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.
1. The mean points is the sample points and has a value of 108 points.
2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.
3. This is a hypothesis test for the population mean.
The claim is that the mean score is significantly less than 110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=108.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{10}}=1.9[/tex]
4. Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{108-110}{1.9}=\dfrac{-2}{1.9}=-1.05[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-1.05)=0.1597[/tex]
As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly less than 110.
11. Little Sally Walker has a choice between going to an in-state college where she would pay
$3,500 per year for tuition or an out of state college where she would pay $6,000 per year. The
cost of living at the in-state college is $700 per month in rent. The out of state college is $400
per month in rent. Assuming all the other factors are equal,
a. what is the yearly expense of the in-state college?
b. what is the yearly expense of the out-of-state college?
Answer:
Step-by-step explanation:
Lets calculate first for in state college
yearly tuition fees = $3,500
monthly living expense = $700
one year has 12 months so yearly living expense =$700 * 12 = $8,400
Yearly expense of the in state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $3,500 + $8,400 = $11,900
____________________________________________________
Lets calculate first for out of state college
yearly tuition fees = $6,000
monthly living expense = $400
one year has 12 months so yearly living expense =$400 * 12 = $4,800
Yearly expense of the out of state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $6,000 + $4,800 = $10,800
____________________________________________________
All else being equal, a study with which of the following error ranges would be
the most reliable?
A. +12 percentage points
B. 117 percentage points
C. +2 percentage points
D. 17 percentage points
Any help would be greatly appreciated
Answer:
the answer is letter B for ur question
Answer:
A. 44,130
B. 44,100
C. 44,000
Step-by-step explanation:
1-4 round down to 0 do not change the desired place value| 5-9 round the desired place value up by one.
Tens (10) Hundreds (100) Thousands (1000)
What is the most important difference between an experiment and an observational study? An experiment is conducted in a laboratory and an observational study is conducted outside. An experiment has a treated group and a control group while an observational study does not. In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention. In an experiment, the researcher studies the effects of medical treatments or other scientific results, while an observational study looks at subjects in the social science arena.
Answer:
In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
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In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention.
What is an experiment?An experiment is designed to test the effect of an intervention or treatment on a particular outcome, by comparing the results from a group that receives the intervention to a control group that does not receive the intervention. In this way, the experiment can establish cause-and-effect relationships and determine if the treatment has a significant effect.
On the other hand, an observational study does not involve any manipulation of the independent variable. It simply observes and records the relationship between variables. Observational studies cannot establish cause-and-effect relationships and the results may be subject to confounding variables, which can make it difficult to interpret the findings.
Hence, the correct answer would be an option (C).
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Rayan Company has 420, 000 shares of $ 10 par. 3 value ordinary shares outstanding. During the year Rayan declared a 5% share dividend when the market price of the shares was $ 36 per share. Three months later Rayan declared a $. 60 per share cash dividend. As a result of the dividends declared during the year, retained earnings [* decreased by
Answer:
The retained earnings decreased by $1,020,600
Step-by-step explanation:
Given that Rayan Company has 420,000 shares of $ 10 par. Rayan then declared a 5% share dividend when the market price of the shares was $36 per share.
Let's calculate the shares issued as stock dividends below:
Issued shares = stock dividends * outstanding shares
= 5% * 420,000
= 21,000
21,000 shares were issued.
Let's calculate the stock dividends.
Stock dividends = issued shares * market price per share
= 21,000 * $36
= $756,000
Stock dividends is $756,000
Let's calculate the amount of cash dividends, since the company declared a $0.60 per share cash dividend after 3 months. We have:
Cash dividend = cash dividend per share * new number of shares.
= $0.60 * (420,000 + 21,000)
= $0.60 * 441,000
= $264,600
Cash dividends paid is $264,600
The find the decrease in retained earnings, we have:
Decrease in Retained earnings = cost of stock dividend + cash dividend.
= $756,000 + $264,600
= $1,020,600
Therefore, the retained earnings decreased by $1,020,600
Please answer this correctly I want helping hand people to answer this correctly
Answer:
w = 36
Step-by-step explanation:
You can make a ratio 98 : 84 = 42 : w
[tex]\frac{49}{42}=\frac{42}{w}[/tex]
49w = 1764
w = 36
A right triangle has sides of integer lengths a, 40, and 41. Find a.
b) 9
c) 141-140
d) -9
a) 1
e) none of these.
Answer:
b) 9
Step-by-step explanation:
9 squared + 40 squared = 41 squared, which follows Pythagorean theorem.
Choose an appropriate metric unit for the capacity of a bottle of ink.
Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and side is 4.
The triangle is missing, so i have attached it.
Answer:
1)sin(α) = 4/7
2)cos(β) = 4/7
3)tan(α) = 4/√33
4)cot(β) = 4/√33
5)sec(α) = 7/√33
6)csc(β) = 7/√33
Step-by-step explanation:
(1) sin(α)
From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.
Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7
2) cos(β)
Cosine of an angle = adjacent side/hypotenuse.
In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7
3)tan(α)
tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.
Using the pythagoras theorem,
Adjacent side = √(7² - 4²)
Adjacent side = √(49 - 16)
Adjacent side = √33.
Thus, tan(α) = 4/√33
4) cot(β)
cot of an angle is the reciprocal of tangent of same angle.
The adjacent side to β is 4 while the opposite is √33.
So, tan(β) = (√33)/4
cot(β) = 1/tan(β)
cot(β) = 1/[(√33)/4]
cot(β) = 4/√33
5)sec(α)
sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.
Thus, sec(α) = 1/cosα = 7/√33.
6) csc(β)
Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.
Thus, csc(β) = 1/sin(β) = 7/√33
