A freight train travels 210 miles in the same amount of time a car travels 330 miles. If the rate of the car is 20 mph more than the rate of the train, find the rate of each.

Answer:

44.38%

Step-by-step explanation:

Becuase of 365 days a year, 162 out of 365 is 44.38% meaning that if he would selwcted a fay the probability would be 44.38% chance.

Answer:

True

Step-by-step explanation:

In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed

Answer:

True

Step-by-step explanation:

In 1 h, the level in the pond increases 1 ft. One way to find how many feet the level increases in 30 min is to multiply One way to find how many inches the level increases in 2- h is to multiply 2. 2 of 5 Completed so that is ture

SOLUTION

The image below will help in answering the following questions

Now, from the graph, the parts above the horizontal line represents profit, while the part below the horizontal line represents loss.

(a) Maximum profits are earned when there are 4 clerks working.

From the graph, we can see that this statement is CORRECT. The maximum profit is at 400 thousand dollars and takes place at 4 on the horizontal axis, this 4 represents 4 clerks working

(b) The store earns profits when no clerks are working.

No clerks are working when we consider 0 on the horizontal plane. From the picture above, tracing 0, it shows us something below the horizontal line which represents loss. So, this statement is INCORRECT. When no clerks work, there is a loss not profit

(c) Maximum profits are earned when there are 7 clerks working.

Tracing 7 from the graph, it doesn't fall on the top part of the curve which indicates maximum profit. Hence, this statement is INCORRECT.

d) The store earns about $400,000 in profits on its best days.

From the image above, we can see that this is correct.

(e) The store loses money when 8 or more clerks are working.

When we traced 8 from the horizontal line, it fell to the part of the graph which indicated loss.

Hence this is CORRECTstatement .

So you will select the 1st, 4th and 5th options

The converse statement is 'If an angle is not a right angles, then it is obtuse' True. Option A

The converse of a conditional statement is formed when the hypothesis and conclusion are both reversed.

In this case, the hypothesis is taken as the conclusion and the conclusion made the hypothesis.

The conditional statement is written as: a → b

The converse is written as b → a

Where;

Given that:

Original statement :Obtuse angles are not right angles

The converse statement : If an angle is not a right angles, then it is obtuse

We can see that the converse statement is true because an obtuse angle is an angle greater than 90 degrees.

Hence, the converse statement is true

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We need to know about scientific notation to solve this problem. The number of seconds the playlist will play is 3.99 x 10^5.

Expressing a number in scientific notation means writing the number as a multiple of ten with ten raised to some power. We use scientific notation for numbers that are very small or very big. When writing numbers in scientific notation we always have one number other than zero before the decimal point. In this question we know that there are 1900 songs and each song has average time of 3.5 minutes, we need to convert the minutes into seconds and multiply the number of seconds of each song to 1900.

1 min=60 seconds

3.5 mins=3.5 x 60=210 seconds

210 x1900=399000 seconds

399000=3.99 x 10^5

Therefore the number of seconds that the playlist will play is 3.99x 10^5

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The ratio of the simplest form of 2 nickels to 1 quarter is 2:5.

For the given question;

The two monetary values are given as;

2 nickles and 1 quarter.

We know that;

1 nickles = 0.2 quarter.

For 2 nickles multiply both side by 2.

2 nickles = 2×0.2 quarter.

2 nickles = 0.4 quarter.

Find the ratio;

2 nickels to that of 1 quarter

2 nickels/ 1 quarter

Put the value of 2 nickle.

2 nickels/ 1 quarter = 0.4 quarter/1 quarter

2 nickels/ 1 quarter = 2/5

2 nickels: 1 quarter = 2:5

Thus, the ratio of 2 nickels to that of 1 quarter is found as 2:5.

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Answer/Step-by-step explanation:

                    3

y + 5 = ( - ) ------- (x - 8)

                    4

                    3

y + 5 = ( - ) ------- x + 6

                    4

                    3

y + 5 = ( - ) ------- x + 6

    -5             4        -5

              3

y = ( - ) ------- x + 1

              4

m = slope = (-3/4)

b = y-intercept = (0, 1)

----------------------------------------------------------------------------------------------------------

The student's first error was in step 1.

Step 1 should involve plotting a point at (0, 1).

Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).

Step 3, connecting the points with a line was correct.

----------------------------------------------------------------------------------------------------------

I hope this helps!

The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E

The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.

These trigonometric identities includes;

It is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.

The cofunction identities are represented thus;

sin θ = cos(90 - θ)

cos θ = sin(90 - θ)

cot θ = tan(90 - θ)

tan θ = cot(90 - θ)

csc θ = sec(90 - θ)

sec θ = csc(90 - θ)

For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)

Thus, the identity is cot (90 ° - 0)

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The correct cofunction identity for tan 0 is cot (90 ° - 0). Option E.

The cofunction identities are defined as trigonometric functions elaborates the relationship between the trigonometric identities.These trigonometric identities includes; sine,cosine, tangent, cotangent, secant cosecant.

It is crucial to note that the value of a trigonometric function of any specific angle is equivalent to the value of the cofunction of their complementary identities.The cofunction identities are represented thus;

For tan 0, we have that its cofunction identity is expressed as;tan 0 = cot (90 ° - 0)Thus, the identity is cot (90 ° - 0)

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The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.

==========================================================

Explanation:

Let's go over an example. We'll have these two sets

A = {1,2}

B = {3,4}

The cartesian product is this set of ordered pairs

A x B= {(1,3), (1,4), (2,3), (2,4)}

Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.

If we swap the order of set A and B then we have

B x A = {(3,1), (4,1), (3,2), (4,2)}

We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.

Side note: Two sets are equal when they are subsets of each other.

Answer:400.98 miles on one full tank

Step-by-step explanation:

you take 32.6 and multiply it by 12.3

The answer as a simplified fraction in the box is -1/6

Given the expression

[3-|-5/6 -2(-1/3)|] ÷ (-17)

Using PEDMAS

P is for parenthesis

[3-|-5/6+2/3)|] ÷ (-17)

[3-|2/3 - 5/6)|] ÷ (-17)

[3-|(4-5)/6)|] ÷ (-17)

[3-|-1/6)|] ÷ (-17)

Since the modulus of a negative number is equal to a positive number, the result will give:

[3 - 1/6] ÷ (-17)

[(18-1)/6] ÷ (-17)

17/6  ÷ (-17)

Next is to carry out the division operation

17/6  × (-1/17)

= -1/6

Hence, The answer as a simplified fraction in the box is -1/6

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The lake is 12,250 feets deep.

The elevation is changing in the downward direction and at a rate of -11ft/s.

So it means that the downward velocity of the probe is 11ft/s.

The value of downward acceleration is 9.8?m/s² which is equal to acceleration due to gravity.

The total time taken to reach down is 50seconds.

We can use the equation of motion because the acceleration is constant,

Using,

S = ut + 1/2at²

Where,

S is the depth of the pool,

U is initial velocity,

U is zero because the probe is dropped.

S = 1/2at²

S = 1/2××9.8×50×50

S = 12250 feets.

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SOLUTION:

Case: Circle equations

Metho:

Given:

Final answer:

Center (-11, 6)

radius, r= 3

Answer:

Step-by-step explanation:

Let f be the number of french fries in the lunch

Let c be the number of chicken wings.

Then, if Leila wants her child to eat less than 600 calories and each french fry has 25 calories and each chicken wing has 100 calories. The linear inequality that represents this situation:

Answer:

43

Step-by-step explanation:

Applying the formula for the area of a rectangle, the  area of the shaded region is calculated as: 42 units².

A rectangle has two pairs of opposite sides that are of equal length, one pair is the length, while the other is the width.

The area of a rectangle = the product of its length and its width = (length)(width).

The area of the shaded region = area of the larger rectangle - area of the smaller rectangle

Dimensions of the larger rectangle:

Length of the larger rectangle = 10 + 2 = 12 units

Width of the larger rectangle = 9 + 2 = 11 units

Area of the larger rectangle = (12)(11) = 132 units²

Dimensions of the smaller rectangle:

Length of the smaller rectangle = 10 units

Width of the smaller rectangle = 9 units

Area of the smaller rectangle = (10)(9) = 90 units²

The  area of the shaded region = 132 - 90

The  area of the shaded region = 42 units²

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The distance between line y= -x-3 and the point (2,5) is  5√2units.

The distance(d) between the line ax+by+c=0 and point (x₁,y₁) is calculated using the formula

d= |ax₁+by₁+c|/√a²+b² , where a and b are the coefficients of x and y .

In the question ,

the equation of the line ℓ is given by y = -x-3

rewriting the equation in standard form  x+y+3=0

So the distance between the line x+y+3 and the point (2,5) can be calculated by substituting the values in the formula, we get

d=|1(2)+1(5)+3|/√1²+1²

= |2+5+3|/√2

= 10/√2

Simplifying further , we get

= 5√2

Therefore , the distance between line y= -x-3 and the point (2,5) is 5√2 units.

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a )  P = { a , n , c , d }

b ) {4 , 7} ⊆ { 4,7,8,12}

c ) {0,1} ⊄ { 1,4,5,6}

are the equations is mathematical symbols

Subsets are a component of the mathematical concept of sets. A set is anything that is contained in curly brackets, as "a,b,c,d." If set B includes the numbers 2, 4, and 6, it is said to be a subset of set A, and if set A is a collection of even integers, it is said to be the superset of set B.

a )  P = { a , n , c , d }

b ) {4 , 7} ⊆ { 4,7,8,12}

c ) {0,1} ⊄ { 1,4,5,6}

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Given that ΔABC is similar to ΔDFE , the value of x = 5.83 (rounded off to hundredth place)

Comparing the given pair of similar triangles,

A ↔ D

B ↔ F

C ↔ E

Now since the ΔABC ~ ΔDFE, the ratio of their sides are equal.

=> [tex]\frac{FE}{BC} = \frac{DF}{CA}[/tex]            (by property of similarity of triangles)

=> [tex]\frac{x}{15} = \frac{7}{18}[/tex]               (substituting respective values)

=> x = 5.83              (simplifying the algebraic equation to hundredth place)

As per the property of similarity of triangles, the corresponding sides have fixed ratio. Thus the ratio of two sides of a triangle will be numerically equal to the ratio of two corresponding sides of its similar triangle. Moreover, the corresponding angles of two similar triangles are equal in measure.

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Answer:6 liters of red paint

Step-by-step explanation:

Calculate the first two terms: 34÷6

Calculate the first two terms: 6

Answer:6

Answer:

[tex]9x - 12x \leqslant 9[/tex]

[tex] - 3x \leqslant 9[/tex]

[tex]x \geqslant - 3[/tex]

The inequality sign must be reversed when multiplying or dividing each side of an inequality by a negative number.

Answer:

x=12

Step-by-step explanation:

We are spending $ 0.0263 less every Mello Yello can, therefore it is  the better buy.

What is profit and loss?
Subtract the smaller value from the greater value in order to calculate the profit or loss. The selling price is always higher than the cost price when there is a profit. Selling price minus cost price is profit. In a loss scenario, the cost price is higher than the selling price. Loss = Price Cost

Given,
20 cans of Mello Yello for $4.75
Therefore cost of 1 can of Mello Yello = $4.75 / 20 = $ 0.2375

Also given,
36 cans of Sprite for $9.50
Therefore, cost of 1 can of Sprite  = $9.50 / 36 = $ 0.2638
Therefore, per can we are paying $ 0.0263 less for Mello Yello.

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Complete Question:

Which is the better buy? Circle your answer (show supporting work)

20 cans of Mello Yello for $4.75

36 cans of Sprite for $9.50

The answer to the given question is option A that is only the first equation is an identity.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

Sin θ = 1/Csc θ or Csc θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ

RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ

Thus LHS = RHS and it is given above so 1st equation is an identity.

2) LHS:  11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ

and RHS : 11 cosec^2 θ

since LHS ≠ RHS because the second equation us not an identity.

thus the correct option is A that is Only the first equation is an identity.

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Let us find the third side of the right triangle using the Pythagora's theorem

The missing side is the opposite side because it is facing the angle

Since supplementary angles are two angles with a sum of 180°, then the supplement of ∠WTV is the angle ∠WTZ. Therefore, the answer is the option C.

Answer:

1.50/3 Apples=0.5

That means each apple cost 0.5. If it's in rands gonna be R0.5 or 50 Cents per apple.