Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3

The smaller angle, inside the bold lines, is -90 degrees.

The larger angle, outside the bold lines, is 270 degrees.

Angles can be measured in increments between -90° and 630°.

Two straight lines are considered to be intersecting if they come together at the same point. The intersection of two lines is known as the junction point. When two lines intersect, four angles are produced. The sum of the four angles is always 360 degrees.

Two straight lines that cross one other and produce right angles are called perpendicular lines. There are four right angles created when two perpendicular lines cross.

There are two types of angle connections produced when lines intersect:

Congruent opposite angles

Nearby angles are helpful

The information is

Let O (0, 0) be the origin, where the y and x axes must connect.

Thus, the angles on the four quadrants of the axis are produced.

The fourth quadrant's crossing lines create an angle that is given by For, the anticlockwise measure, A = -90°.

B = 360n - 180° for the clockwise measure, and n = 3 in this case.

Hence, when we simplify, we obtain

The second angle has a length of = 630°.

As a result, the angles are 90° and 630°.

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By completing the square the function will be, g(x)=4(x-2)²-9

The standard form of the quadratic equation will be ax²+bx+c=0.

Equate the given equation with standard form of equation and determine the values of a, b, and c.

a=4

b=-16

c=7

For completing the square, add and subtract [tex]\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16[/tex] in the given equation.

g(x)=4x²-16x+16-16+7

g(x)=(4x²-16x+16)-9

g(x)=4(x²-4x+4)-9

The term x²-4x+4 is equivalent to (x-2)².

g(x)=4(x-2)²-9

So, the given function is same as g(x)=4(x-2)²-9.

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Answer:

  tan(x) = -1/6

Step-by-step explanation:

We can use the relation between tan and sec:

  [tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]

The tangent of x is -1/6.

Answer:

Option d

Step-by-step explanation:

The p-value is 0.0516 which is not statistically significant to reject the null hypothesis. Thus we will fail to reject the null hypothesis.

The image of the stem-and-leaf plots is in the attachment.

Answer: (a) 31 years; (b) 59 years; (c) 56 years

Step-by-step explanation: Steam and leaf is a table that shows the digits of the data value split into a "stem", which represents the first digit, and a "leaf", which is the last digit.

For example, the first row of the table in the attachment, indicate a "stem" 2 and the first number of a "leaf" is 1, so the actress has 21 years.

(a) According to the table, the youngest actor to win an Oscar has a "stem" 3 and the first "leaf" from the right is 1, so the actor has 31 years.

(b) The oldest actress is 80 and the youngest is 21, so difference is:

80 - 21 = 59

The difference is 59 years.

(c) The oldest age shared by 2 actors is 56 years.

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%    

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

Step-by-step explanation:

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let [tex]\mu[/tex] = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                                T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean percentage = 23.2

            s = sample standard deviation = 0.2

            n = sample of specimens = 10

So, the test statistics  =  [tex]\frac{23.2-23}{\frac{0.2}{\sqrt{10} } }[/tex]  ~ [tex]t_9[/tex]

                                     =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

            P-value = P( [tex]t_9[/tex] > 3.162) = 0.006 or 0.6%

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let  = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_o:\mu[/tex]:  = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis,  [tex]H_A:\mu\neq[/tex]:   23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

[tex]TS=\dfrac{X-\mu}{\frac{s}{\sqrt{n}}}[/tex]   ~ [tex]t_{n-1}[/tex]

where,  = sample mean percentage = 23.2

           s = sample standard deviation = 0.2

           n = sample of specimens = 10

So, the test statistics  =   [tex]\dfrac{23.2-23}{\frac{0.2}{\sqrt{10}}}[/tex] ~ [tex]t_g[/tex]

                                    =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

           P-value = P( [tex]t_g[/tex] > 3.162) = 0.006 or 0.6%

Hence ,

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

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Answer:

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Answer:

c

Step-by-step explanation:

Answer:

The age difference between oldest the youngest is of 48 years.

Step-by-step explanation:

We can solve this question using a system of equations.

I am going to say that:

Kissi's age is x.

Esinam's age is y.

Lariba's age is z.

The ratio of the ages of Kissi and Esinam is 3:5

This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]

That of Esinam and Lariba is 3:5

This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]

The sum of the ages of all 3 is 147 years

This means that [tex]x + y + z = 147[/tex]

What is the age difference between oldest the youngest

z is the oldest

x is the youngest.

First i will find y.

We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]

So

[tex]x + y + z = 147[/tex]

[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]

The lesser common multiple between 5 and 3 is 15. So

[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]

[tex]49y = 147*15[/tex]

[tex]y = \frac{147*15}{49}[/tex]

[tex]y = 45[/tex]

Youngest:

[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]

Oldest:

[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]

Difference:

75 - 27 = 48

The age difference between oldest the youngest is of 48 years.

Answer:

The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s

Step-by-step explanation:

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0  

⇒  x2 - 10x + 5x - 50 = 0  

⇒ x (x - 10) + 5 (x - 10) = 0

⇒  (x+5) (x-10) = 0

⇒   (x+5) (x-10) = 0  

⇒ x =  -5 or 10  

⇒ x = 10 (x = -5 , rejected)

Answer:

Option D

Step-by-step explanation:

If these lines are parallel, they should have the same slope. How so? Well slope is the change in axis, y / x more specifically. If the lines are parallel they should change at a similar rate so that they don't intersect, and hence are, by definition, ║;

[tex]Green Line's Slope = Red Line's Slope,\\8 = Red Line's Slope,\\Red Line's Slope = 8 units\\\\Solution - Option D[/tex]

Hope that helps!

Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Answer:

h≤48   h≥30

Step-by-step explanation:

Answer:

Radius of the circle = 6 units

Step-by-step explanation:

Let the radius of the circle be r

According to the given condition:

Area of the circle = 3 times the circumference of the circle

[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]

Answer:

1008

Step-by-step explanation:

to find the number of combinations, just multiply everything. you will get 1008 :)

Answer:

there is significant distinction in opinion regarding abolition of capital punishment.

Step-by-step explanation:

Compute the p cost of 2-proportion for estimating difference. The Minitab output pronounces the p valu eto be 0.000. This is less than the assumed importance degree of alpha = 0.05. Therefore, reject null hypothesis to finish that there is significant distinction in opinion regarding abolition of capital punishment.

Answer:

✅Amanda had a greater percent increase in weight.

Step-by-step explanation:

The percent change in Ryan’s weight was 42/7 or 60%. The percent change in Amanda’s weight was 6.9/6, or 115%. Amanda had a greater percent increase in weight.

IamSugarBee

Answer:

The percent change in Ryan’s weight was 4.2/7, or 60%. The percent change in Amanda’s weight was 6.9/6 , or 115%. Amanda had a greater percent increase in weight.

Step-by-step explanation:

its the sample answer i just did it

Answer:

39 degrees

Step-by-step explanation:

Given

triangle is right angled i.e one angle is 90 degrees

other angle is 51 degrees.

let the third angle be x degrees

we know that sum of angles of any triangle is 180 degrees

thus,

90 + 51+ x = 180

=> 141 + x = 180

=> x = 180 - 141 = 39.

Thus, measure of other small angle is 39 degrees.

Answer:

Step-by-step explanation:

m∠A+m∠B+m∠C = 180

90+51+x1= 180

41+x=180

x=39

Answer:

€ 270

Step-by-step explanation:

Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have  2x² + 5y² + 120 ≤ 250

The selling price S(x,y) = 40x + 80y

The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120

Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.

So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y

dP/dx + λdC/dx = 0

40 - 4x + 4λx = 0  (1)

4λx = 4x - 40

λ = (x - 10)/x

dP/dy + λdC/dy = 0

80 - 10y + 10λy = 0 (2)

substituting λ into (2), we have

80 - 10y + 10(x - 10)y/x = 0

multiplying through by x, we have

80x - 10xy + 10xy - 100y = 0

80x - 100y = 0

80x = 100y

x = 100y/80

x = 5y/4

substituting x into C(x,y) ≤ 250, we have

2(5y/4)² + 5y² + 120 ≤ 250

25y²/8 + 5y² + 120 ≤ 250

25y² + 40y² + 960 ≤ 2000

65y² ≤ 2000 - 960

65y² ≤ 1040

y² ≤ 1040/65

y² ≤ 16

y ≤ ±√16

y ≤ ± 4 since its quantity, we take the positive value.

So x = 5y/4 = 5(± 4)/4 = ± 5

So, x ≤ ± 5

For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have

P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120

= 200 + 320 - 50 - 80 - 120

= 520 - 250

= 270

So, the maximum profit obtained is € 270

Answer:

Step-by-step explanation:

Corresponding net sales before 1 month and after 1 month form matched pairs.

The data for the test are the differences between the net sales before and after 1 month.

μd = the​ net sales before 1 month minus the​ net sales after 1 month.

Before after diff

57.1 63.5 - 6.4

94.6 101.8 - 7.2

49.2 57.8 - 8.6

77.4 81.2 - 3.8

43.2 41.9 1.3

Sample mean, xd

= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94

xd = - 4.94

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872

Standard deviation = √(60.872/5

sd = 3.49

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (- 4.94 - 0)/(3.49/√5)

t = - 3.17

We would determine the probability value by using the t test calculator.

p = 0.017

Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.

Answer:

416

Step-by-step explanation:

plz mark brainliest!

Answer:

385

Step-by-step explanation:

use l x w

14x19

16x3

7x10

385

Answer:

[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]

The variance would be given by:

[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]

And the deviation would be:

[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]

Step-by-step explanation:

For this case we have the following distribution given:

X      1      2      7

P(X) 1/5  2/5   2/5

We need to begin finding the mean with this formula:

[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(X) =1 *\frac{1}{5} +2 *\frac{2}{5} +7*\frac{2}{5}= 3.8[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]

And replacing we got:

[tex] E(X^2) =1^2 *\frac{1}{5} +2^2 *\frac{2}{5} +7^2*\frac{2}{5}= 21.4[/tex]

The variance would be given by:

[tex] Var(X) =E(X^2) -[E(X)]^2 = 21.4 -[3.8]^2 = 6.96[/tex]

And the deviation would be:

[tex] Sd(X) =\sqrt{6.96}= 2.638[/tex]

Answer:

24 ounces of orange juice

Step-by-step explanation:

Given-

          Calories needed=390 calories

    Calories in 8oz juice=130 calorie

Therefore ounces of juice=(390/130)8

                                          =3 x 8

                                          =24 ounces

If Ronald needs a morning breakfast drink that will give him atleast 390 calories. Orange juice has 130 calories in 8oz. Then 24 ounces does he need to drink to reach his calorie goal.

Two or more expressions with an Equal sign is called as Equation.

Ronald needs a morning breakfast drink that will give him at least 390 calories.

Orange juice has 130 calories in 8oz.

We need to find how many ounces does he need to drink to reach his calorie goal

Calories needed=390 calories

Calories in 8oz juice=130 calorie

Three hundred ninety divided by one hundred thirty times of eight.

Therefore ounces of juice=(390/130)8

Three hundred ninety divided by one hundred thirty is three.

=3 x 8

Three times of eight is twenty four.

=24 ounces

Hence 24 ounces of orange juice does he need to drink to reach his calorie goal.

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Answer:

The answer is 508

Step-by-step explanation:

Solution

First of all, the proportion of B is exceeds 0.5 in total.

Now,

To find the total of A it we have A =314 +512 = 826

The number of employed that choose B = 356

For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed

what this suggest is that the employed B is greater than 826-356 = 470

So,

The respondent that are unemployed that choose B  must be greater than 470

Thus,

We recall that the B proportion among the unemployed respondent is lesser than .50

Thus suggests that the respondent that are unemployed who choose be is lesser than 512

The conditions becomes

470 lesser than the number of unemployed respondents who selected B lesser than 512

Hence  the needed number of the number of unemployed respondents who chose B should be between 470 and 512

So, possible answer here is 508.

Answer:

c & d

Step-by-step explanation:

the description matches the information in the table

Answer: A, B, C

Step-by-step explanation:

domain = x

range = y

Answer:

$2350

Step-by-step explanation:

If 94 is 4%, multiply it by 25 to get $2350, or 100%

the cost of the item is $ 2350.

To find the cost of the item, we can set up an equation using the information given.

Let's denote the cost of the item as $ x.

According to the given information, the sales tax on the item is 4 % and is equal to $ 94. We can express this as:

0.04 x = 94

To solve for x, we divide both sides of the equation by 0.04:

x = tax on item / sales tax

x = 94 / 0.04

x = 2350

Therefore, the cost of the item is $ 2350.

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Answer:

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $79.20

Standard deviation r = $10.41

Number of samples n = 14

Confidence interval = 90%

Using the z table;

The critical value that should be used in constructing the confidence interval.

z(α=0.05) = 1.645

Critical value at 90% confidence z = 1.645

Substituting the values we have;

$79.20+/-1.645($10.42/√14)

$79.20+/-1.645($2.782189528308)

$79.20+/-$4.576701774067

$79.20+/-$4.577

( $74.623, $83.777)

The 90% confidence interval is = ( $74.623, $83.777)

Answer:

y=3x-7

Step-by-step explanation:

lines are parallel hence gradient from the equation in question is the same as the gradient of the equation to be found.. comparing to y=mx+c, eq in question has grad 3... from the formula y-y1=m(x-x1) where (x1,y1) is equal to the point in question

Answer:

Make That Guy Brainliest Now ^^^^^    You can now that there are two answers!

Step-by-step explanation:

Hope this helps

Hope this is correct

Answer:

F = 95°

Step-by-step explanation:

[tex]C=\frac{5}{9}(F-32)[/tex] is the formula to convert Fahrenheit to Celsius

If we have C = 35, we just need to plug in this number to its corresponding variable and then solve for F