Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! How much pure water should she add to have a 10% syrup?

Answer:

The given number is 3.441

The first 4 is in the tenth place that is written like [tex]\frac{4}{10}[/tex] or 0.4

The second 4 is in the hundredth place that is written like [tex]\frac{4}{100}[/tex] or 0.04

We can see that the second 4 is one tenth times the first 4. This is shown like = [tex]\frac{1}{10} \times\frac{1}{10}[/tex] = [tex]\frac{1}{100}[/tex]

Or we can say the opposite that the first 4 is ten times the second 4.

Using the place value chart, we can see that the decimal 0.8 is eight-tenths, so we can write 0.8 as the fraction [tex]\frac{8}{10}.[/tex] We are able to simplify so we will divide the numerator and the denominator by 4.

Image is provided.

Therefore, the decimal 0.8 can be written as [tex]\frac{4}{5}[/tex].

Answer:

4/5

Step-by-step explanation:

0.8=8/10=4/5

Final answer:

To factor the polynomial [tex]8t^2 + 8t - 72,[/tex]  we first extract the common factor of 8, then factor the trinomial [tex]t^2 + t - 9[/tex] using the technique of finding two numbers that multiply to -72 and add up to 1, which are 9 and -8. Finally, we group and factor by grouping to get the factored form, 8(t - 8)(t + 9).

Explanation:

To factor the polynomial  [tex]8t^2 + 8t - 72,[/tex], we will first look for the common factors and then apply factoring techniques. First, we can take out the common factor of 8:

8[tex](t^2 + t - 9)[/tex]

Next, we factor the trinomial inside the parentheses. We need two numbers that multiply to 8 * -9 = -72 and add up to 1. These numbers are 9 and -8. So, we can split the middle term based on these numbers:

[tex]t^2 - 8t + 9t - 9[/tex]

We group the terms to factor by grouping:

Now we factor out the common binomial factor:

(t - 8)(t + 9)

Therefore, the factored form of  [tex]8t^2 + 8t - 72,[/tex] is 8(t - 8)(t + 9).

The stamp collector purchased 40 5¢ stamps, 120 15¢ stamps, and 0 25¢ stamps.

To solve this problem, let's assign variables to the number of each type of stamp purchased. Let x be the number of 5¢ stamps, y be the number of 15¢ stamps, and z be the number of 25¢ stamps. We are given that the number of 15¢ stamps is three times the number of 5¢ stamps, so we can write this as y = 3x. We also know that the total number of stamps is 160, so we have the equation x + y + z = 160.

Using these equations, we can set up a system of equations:

y = 3x

x + y + z = 160

We can substitute the first equation into the second equation to eliminate y:

x + 3x + z = 160

Combining like terms, we get 4x + z = 160. We can rearrange the equation to solve for z:

z = 160 - 4x

Now we can substitute this expression for z back into the second equation:

x + 3x + 160 - 4x = 160

Simplifying, we get 4x = 0. Solving for x, we find x = 40. Plugging this value back into the equation y = 3x, we get y = 120. Finally, we can find z by substituting x and y into the equation z = 160 - 4x:

z = 160 - 4(40) = 160 - 160 = 0.

So, 40 5¢ stamps, 120 15¢ stamps, and 0 25¢ stamps were purchased.

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Answer:

9

Step-by-step explanation:

Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The probability of an event is a number between [tex]0[/tex] and [tex]1[/tex], where, roughly speaking, [tex]0[/tex] indicates the impossibility of the event and [tex]1[/tex] indicates certainty.

Since,  [tex]\frac{2}{7}[/tex]  is the probability that the first satellite sends a weak signal.

And leaves six, and one is sending a weak signal.

So, the probability that the second also sends a weak signal it has the probability [tex]\frac{1}{6}[/tex].

By Combining these and we get

[tex]\frac{2}{7}[/tex]×[tex]\frac{1}{6}[/tex] = [tex]\frac{1}{21}[/tex] .

Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]

To know more about probability

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Answer: $1.98

Step-by-step explanation:

Given: The total amount Tanya spent on cans of tuna = $8.15

Also, she used a coupon that gave her 35 cents off each can.

Therefore, The total discount on 5 cans =[tex]5\times35=175\ cents[/tex]

Since, $1=100 cents or 1 cent= 0.01 dollar

Therefore, the total discount on 5 cans=[tex]0.01\times175=\$1.75[/tex]

Now, the price of 5 cans of tuna without the coupon=[tex]\$8.15+1.75=\$9.90[/tex]

The price of a can of tuna without the coupon=[tex]\frac{9.90}{5}=\$1.98[/tex]

[tex]\huge{\boxed{47}}\ \ \huge{\boxed{48}}[/tex]

First, represent the situation with numbers and variables. The first number will be [tex]x[/tex] and the second number will be [tex]x+1[/tex]. [tex]x+x+1=95[/tex]

Combine like terms. [tex]2x+1=95[/tex]

Subtract 1 on both sides. [tex]2x=94[/tex]

Divide both sides by 2. [tex]x=\boxed{47}[/tex]

Find the second number. [tex]x+1\ =\ 47+1\ =\ \boxed{48}[/tex]

To find the distance between the high school at (17,21) and the town park at (28,13), use the distance formula which yields a result of approximately 13.6 miles apart, rounded to the nearest tenth.

When looking at the coordinates of the high school at (17,21) and the town park at (28,13) on a coordinate grid where each unit represents 1 mile, we need to use the distance formula to calculate the distance between the two points. The distance formula is derived from the Pythagorean theorem and is given by:

[tex]Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

Substituting the values -

[tex]Distance = \sqrt{{(28 - 17)^2 + (13 - 21)^2}[/tex]

Calculate the differences and square them:

Distance = [tex]\sqrt{{(11)^2 + (-8)^2}\\[/tex]

Distance = [tex]\sqrt{{121 + 64}[/tex]

Distance = [tex]\sqrt{{185[/tex]

Take the square root to find the distance:

Distance = 13.6 miles

Therefore, the high school and the town park are approximately 13.6 miles apart, rounded to the nearest tenth.