A triathlon athlete swims at an average rate 2.4 miles per hour, and bikes at an average rate of 16.1
miles per hour. At the end of one training session, she has swum and biked more than 20 miles in
total.
The inequality 2.4s + 16.16 > 20and this graph represent the relationship between the hours of
swimming, s, the hours of biking, b, and the total distance the athlete could have traveled in miles.
hours of biking
N
8
10
2 4 6 8
hours of swimming
Mai said, "I'm not sure the graph is right. For example, the point (10,3) is in the shaded region, but
it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think
triathlon athletes generally train for no more than 2 hours a day."

Answer:

x = 19

Step-by-step explanation:

In the attached file

In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.

Congruency Requirements:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side) 

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The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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Yes and opposite and an absolute value of an integer will be the same.

Answer:

Your answer is 660.47 :)

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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Answer:

3 days

Step-by-step explanation:

Given that :

Today :

Study time for math = 15 minutes

Study time for science = 75 minutes

Subsequent days :

Study time for math = 50 minutes

Study time for science = 30 minutes

Let the number of days when study time for math and science will be the same = x

15 + 50x = 75 + 30x

50x - 30x = 75 - 15

20x = 60

x = 60 / 20

x = 3

3 days

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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Answer:

According to theorem 7.5

Π ABB'A' ≅ Π DEE'D'  

therefore by transitivity of equivalence  it is proven that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides

Step-by-step explanation:

To prove that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides :

Assume:  б(Δ ABC ) =  б(Δ DEF ) and also AB ≅ DE

let Π ABB'A' and DEE'D' be taken as the saccheri quadrilaterals that corresponds to Δ ABC and Δ DEF  respectively

Following the Lemma above; б(Π ABB'A' ) = б( Π DEE'D' ) given that

AB = summit of ABB'A' and DE = summit of DEE'D'  also  AB ≅ DE

According to theorem 7.5

Π ABB'A' ≅ Π DEE'D'  

therefore by transitivity of equivalence  it is proven that triangle ABC and triangle DEF are triangles with equal defects and a pair of congruent sides

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

\(x^\frac{2}{3}\)

Step-by-step explanation:

Using the power of power rule (multiply the exponents)

\(x^\frac{4}{3}\) × \(^\frac{1}{3}\)       \(x^\frac{2}{3}\) × \(^\frac{1}{3}\)

\(x^\frac{4}{9}\)            \(x^\frac{2}{9}\)

When exponents are multiplied, add the answers:

x ^ ( 4/9 + 2/9 )

x ^ ( 6/9 )

x ^ ( 2/3 )

Answer: I think the greatest common factor is 4x^2

Step-by-step explanation:

Find the numerical common factors. Which are 8, -12, and 20. Find the variable common factors for x^4, x^3, and x^2. Multiply them together. Then break down the factors on both sides and pick the biggest one. Finally multiply them together. (I’m sorry, I’m very bad at explaining things.)

Answer:

True

Step-by-step explanation:

If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots

If the discriminant \(D=b^2-4ac > 0\), then there are two real roots

If the discriminant \(D=b^2-4ac=0\), then there is only one real root

31 and 35.

Sure hope this helps you

Answer:

Expression: 40x+35

40(10)+35= $435

Step-by-step explanation:

There are 12 months, and we want to use the cellphone company for 10 months.

Let x represent months, and put 40 in front because that's the monthly charge for each month.

Next add 35 as your initial value to the expression.

When you go in the equation, 40 multiplied by 10 is 400.

400 plus 35 is 435.

So, $435 will be charged for 10 months of service.

Answer:

23

Step-by-step explanation:

3x = 69°

This is because they are vertically opposite angles.

You would have to divide 69 by 3.

69 ÷ 3 = 23

23 · 3 = 69

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) 25

(c) 84700

(d) 70

(e) b < 25

Step-by-step explanation:

(a) Independent variable:  b (number of bags sold)

    Dependent variable:  p(b)  (profit)

(b) To break even, set p(b) to zero and solve for b:

⇒ 350b - 8750 = 0

⇒ 350b = 8750

⇒ b = 8750 ÷ 350

⇒ b = 25

(c) Substitute b = 267 into equation and solve for p(b):

⇒ 350(267) - 8750 = 84700

(d) Set p(b) to 15750 and solve for b:

⇒ 350b - 8750 = 15750

⇒ 350b = 15750 + 8750

⇒ 350b = 24500

⇒ b = 24500 ÷ 350

⇒ b = 70

(e) If she breaks even when she sells 25 bags, if she sells less than 25 bags she will have a negative profit. So b < 25

Answer:( 175/6)

Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35

Answer:

(0, -9)

Step-by-step explanation:

The y intercept is the y value when x =0

(0, -9)

Answer:

Step-by-step explanation:

Take angle A as reference angle

using sin rule

sin A=opposite/hypotenuse

sin A=10/13

sin A=0.76

\(sin^{-1}\) 0.76=49.46 degree

A=49.5 degree

Answer:2.

Step-by-step explanation:

trust me on this one

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

here

Step-by-step explanation:

2.000.000.099

In a case whereby Anu was checking her emails and she casually told her friend siting next to her the ratio of unread emails in my inbox is ratio 4:1 where the total number of emails is 120  then the number of unread emails in her inbox is 96mails.

The concept that will be used here is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The total mails in her box is 120

The we can represent the unread mails  as 4x and read mails be 1x

This can be expressed as :

(4x+1x)=120mails

5x=120mails

x=120/5

x=24

This implies that the uread mails(4×24)

=96mails

Then the number of the read mail =(1×24)=24mails

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Answer:

90 years

Step-by-step explanation:

if Kripa's age = x

Father's age = x + 40

Grandfather's age = (x + 40) + 35 = x + 75 (father is 35 years younger than grandfather i.e. grandfather is 35 years older than father)

x + x + 40 + x + 75 = 160

=> 3x = 160 - 115

=> x = 45/3 = 15

grandfather's age = x + 75 = 90 years

Answer:

Step-by-step explanation:

x + x + 40 + x + 75 = 160

=> 3x = 160 - 115

=> x = 45/3 = 15

Grandfather's age = x + 75 = 90 years

Answer:

n=22.23

Step-by-step explanation:

21+n=43.23

-21 to both sides

0+n=22.23

n=22.23

Answer:

Step-by-step explanation:

y = ax² + bx + c

Plug the points into the equation to get a system of 3 equations with 3 unknowns a, b, and c.

-27 = 4a - 2b + c

-42 = 9a + 3b + c

-12 = a + b + c

(a,b,c) = (-4,1,-9)

y = -4x² + x - 9