a sprinter travels a distance of 300m in a time of 26.24 seconds. what is the sprinters avarage speed round to 4 sf?

Heather has divided $5400 between two investments, one paying 8%, the other paying 5%. if the return on her investment is $

Phantasy [73]

Answer:

$2500 at 8%.

$2900 st 5%.

Step-by-step explanation:

Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.

We have been given that Heather has divided $5400 between two investments. We can represent this information as:

$x+y=5400...(1)$

The return on her investment is $345.

Earnings from the investment at 8% will be 8% of x.

Earnings from the investment at 5% will be 5% of y.

$(\frac{8}{100})x+(\frac{5}{100})y=345...(2)$

$0.08x+0.05y=345...(2)$

We will use substitution method to solve our system of equations. From equation (1) we will get,

$x=5400-y$

Substituting this value in equation (2) we will get,

$0.08(5400-y)+0.05y=345$

$432-0.08y+0.05y=345$

$-0.08y+0.05y=345-432$

$-0.03y=-87$

$\frac{-0.03y}{-0.03}=\frac{-87}{-0.03}$

$y=2900$

Therefore, Heather has invested an amount of $2900 at 5%.

Let us substitute y=2900 in equation (1) to solve for x.

$x+2900=5400$

$x+2900-2900=5400-2900$

$x=2500$

Therefore, Heather has invested an amount of $2500 at 8%.

6 0

3 years ago

Susan paid $15.84 for a 7.48 - kg bag of dog food. A few weeks later, she paid $16.58 for a 7.94 - kg bag at a different store.

barxatty [35]

The unit price for the 7.48 is $2 kg per bag and the unit price for the 7.94 is $2 per kg bag, there is no difference in unit rates of both the bag.

A unit rate means a rate for one of something.

Given that, Susan paid $15.84 for a 7.48 kg bag of dog food. A few weeks later, she paid $16.58 for a 7.94 kg bag at a different store.

15.48/7.48 = $2/kg

16.58/7.94 = $2/kg

Hence, there is no difference in between both the bags, hence either of them are better.

For more references on unit rates, click;

brainly.com/question/11258929

#SPJ1

4 0

1 year ago

Help me pleasseeeee!!! its about algebraic properties of limits!

s2008m [1.1K]

$\text{Hello there! :)}$

$3. \sqrt{2} \\\\\text{4. 0}\\\\\text{5. dne}$

$\text{To find the overall limit, they must approach the same y-value from each side:}$

$\\\\3. \lim_{x \to \frac{\pi }{4} } 2sinx ={\sqrt{2}$

$\text{Therefore:}\\\\3. \lim_{x \to \frac{\pi }{4} } f(x)= {\sqrt{2} }$

$\text{For this question, evaluate the limit from the RIGHT-HAND side:}\\\\4. \lim_{x \to \pi +} f(x)\\\\ \text{Use the equation tanx to evaluate since it involves values greater than \pi:}\\\\$

$\lim_{x \to \pi +} tanx = 0\\\\\text{So:}\\\\ \lim_{x \to \pi +} f(x) = 0$

$5. \\\\\text{Evaluate the overall limit. Make sure both sides approach the same y=value:}\\\\ \lim_{x \to \pi } 2cosx= -2\\\\ \lim_{x \to \pi } tanx = 0\\\\ \text{ Therefore:}\\ \lim_{x \to \pi } f(x) = dne \text{ (Does not exist})$

5 0

3 years ago

The Venn diagram shows event A and event B comprised of outcomes from the same sample space. The probability of event A is given

Masteriza [31]

Answer:

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1

A=45

Step-by-step explanation:

7 0

3 years ago

Solve the inequality for x. show each step of the solution -12x-0.4>0.2(36.5x+80)-55

Darina [25.2K]

Let's solve your inequality step-by-step.

−12x−0.4>0.2(36.5x+80)−55

Step 1: Simplify both sides of the inequality.

−12x−0.4>7.3x−39

Step 2: Subtract 7.3x from both sides.

−12x−0.4−7.3x>7.3x−39−7.3x

−19.3x−0.4>−39

Step 3: Add 0.4 to both sides.

−19.3x−0.4+0.4>−39+0.4

−19.3x>−38.6

Step 4: Divide both sides by -19.3.

−19.3x

−19.3

>

−38.6

−19.3

x<2

Answer:

x<2

8 0

3 years ago