Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation:  . What did he define as the variable x?

The shortest distance they travel to return to starting point is 9.43 miles.

Since, two joggers run 8 miles north and then 5 miles west.

According to question , a right triangle is formed. and hypotenuse of right triangle represent the shortest distance between starting point to final point.

Apply Pythagoras theorem,

             Shortest distance, [tex]=\sqrt{8^{2}+5^{2} } =\sqrt{64+25}=\sqrt{89}=9.43miles[/tex]

Thus, They travel 9.43 miles to return to their starting point.

Learn more:

https://brainly.com/question/11528638

To simplify the expression 4/7 * 5/9, the equivalent expression is 20/63.

To simplify the expression 4/7 * 5/9, we can multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. So, the expression becomes 20/63. Therefore, none of the options listed are equivalent to 4/7 * 5/9.

https://brainly.com/question/27911936

#SPJ12

None of the options a, b or c are equivalent to the expression 4/7*5/9. The correct expression must simplify to 20/63.

The question is asking to find out which of the provided expressions is equivalent to the expression 4/7*5/9. The correct option should yield the same result as the original expression when calculated. The expression 4/7*5/9 simplifies to 20/63.

Let's check the provided options:

The provided information about relative frequencies is irrelevant for this question.

https://brainly.com/question/34140345

#SPJ12

Answer:  11.5 feet

Step-by-step explanation:

Given: The height of Fatim = 6 feet

At noon, he stands with the sun behind him casting a shadow. Also, Fatima is standing vertical to the ground such that a right triangle is formed.

Let the length of Fahim’s shadow be x.

By Pythagoras theorem , we have

[tex]13^2=x^2+6^2\\\\\Rightarrow169=x^2+36\\\\\Rightarrow\ x^2=169-36\\\\\Rightarrow\ x^2=133\\\\\Rightarrow x=\sqrt{133}=11.5325625947\approx11.5[/tex]

Hence, the  length of Fahim’s shadow =11.5 feet

After selling 6 out of 21 granola bars, the store has 15 left. Following a shipment of 42 granola bars, the store will have a total of 57 granola bars in stock.

To find out how many granola bars the store will have in stock after the shipment, we should first calculate how many granola bars are left after the sales by subtracting the number sold from the initial stock. They started with 21 granola bars and sold 6, so they have 21 - 6 = 15 granola bars left. Then, we add the number of granola bars in the shipment arriving tomorrow to the number they currently have in stock. They will receive 42 granola bars in the shipment, so the total will be 15 + 42 = 57 granola bars in stock after the shipment arrives.

The unknown number is equal to 2100.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

"when divided by 3, I am 700."

n/3 = 700  ...equation 1.

n = 700(3)

n = 2100.

"when divided by 7, I am 300."

n/7 = 300 ....equation 2.

n = 300(7)

n = 2100.

Read more on equation here: brainly.com/question/18912929

#SPJ6

Final answer:

A sphere has no vertices as it is a three-dimensional shape with a continuous curved surface, unlike a cube which has distinct edges and flat faces.

Explanation:

The question "how many vertices does a sphere have?" can be answered quite simply. A sphere is a perfect three-dimensional shape where every point on the surface is equidistant from the center. Unlike a cube, which has flat faces and edges, a sphere has a continuous curved surface. Consequently, a sphere does not have any vertices, edges, or faces. Vertices are points where edges intersect, and since a sphere has no edges or flat faces, it cannot have vertices.

Sarah must score at least 44 on her third test in order to have an average of at least 80.

To find out what score Sarah must make on her third test in order to have an average of at least 80, we can set up an equation. The average of her three test scores can be calculated by adding up her scores and dividing by 3:

Average = (98 + 98 + x) / 3

We want the average to be at least 80, so we can solve the equation for x:

(98 + 98 + x) / 3 ≥ 80

Simplifying the equation, we get:

196 + x ≥ 240

Subtracting 196 from both sides, we have:

x ≥ 44

Therefore, Sarah must score at least 44 on her third test in order to have an average of at least 80.

Sarah needs to score at least a 44 on her third test to have an average of at least 80 across her three test scores.

Sarah has grades of 98 and 98 on her first two tests and wants to have an average of at least 80 after her third test. To calculate the minimum score Sarah must make on the third test to achieve her goal, we use the formula for the average of three numbers, which is (test1 + test2 + test3) / 3. In Sarah's case, the average after three tests should be at least 80.

Let's represent the third test score as 'x'. Thus, the equation to find 'x' becomes:

(98 + 98 + x) / 3 ≥ 80

Combining the scores of the first two tests gives us:

(196 + x) / 3 ≥ 80

By multiplying both sides by 3 to eliminate the denominator, we have:

196 + x ≥ 240

Subtract 196 from both sides to solve for x:

x ≥ 240 - 196

x ≥ 44

Therefore, Sarah must score at least a 44 on her third test to achieve an average of 80.