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Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15

Answers

Answer 1

Answer:

Answer:

-3 (removable), +5

Step-by-step explanation:

Maybe you have ...

$f(x)=(x+3)/(x^2-2x-15)=(x+3)/((x+3)(x-5))=(1)/(x-5)\quad x\ne-3$

This will have discontinuities (points where the function is undefined) at ...

x = -3
x = 5

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.

Answer 2

Answer:

Final answer:

The function f(x) = x + 3x² - 2x - 15 is continuous for all x-values.

Explanation:

In order to find the x-values at which the function f(x) = x + 3x² - 2x - 15 is not continuous, we need to look for points where the function has discontinuities. A function can have three types of discontinuities: removable discontinuities, jump discontinuities, and infinite discontinuities.

To find the x-values at which f(x) is not continuous, we need to check for three conditions: 1) The function is defined for all real numbers, so there are no points where f is undefined. 2) The function does not have any jump or jump-like discontinuities, which occur when the left and right limits of a point are finite but not equal. 3) The function does not have any infinite discontinuities, which occur when the left and right limits of a point are infinite.

Therefore, the function f(x) = x + 3x² - 2x - 15 is continuous for all x-values. There are no discontinuities in this function.

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Twice the square of a number

Answers

Answer:

2 * x^2

Step-by-step explanation:

in word form: two times the square of x

"a number" can be any variable; i used x

Answer:

x² × 2

Step-by-step explanation:

Notice vocabulary:

twice → multiplication by a factor of two → ×2
a number → unknown number; variable → x
the square → raised to the power of two → x²

Put this information together.

"Twice the square of a number"

Since it says of a number, this number comes first → $x$

"Twice the square of a number"

The square of a number means that the variable will be squared → $x^2$

"Twice the square of a number"

Multiply the variable by a factor of two → $x^2*2$

:Done

You need 2.5 pounds of potatoes. If each potato weighs 5 ounces, how many potatoes will you need?

Answers

Answer:

40 potatoes.

Step-by-step explanation:

16 ounces make a pound, so you multiply that by 2.5 and you get 40.

Final answer:

You need 8 potatoes to total 2.5 pounds, considering each potato weighs 5 ounces.

Explanation:

To solve this problem, you first need to understand that 1 pound is equal to 16 ounces. So, 2.5 pounds would be 40 ounces (16 ounces/pound x 2.5 pounds). If one potato weighs 5 ounces, you would divide 40 (total ounces needed) by 5 (ounces per potato) to find the number of potatoes needed. Thus, you will need 8 potatoes to get approximately 2.5 pounds.

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According to a medical journal, the average daily U.S. diet contains 6,000 mg of sodium. How many grams is this?

Answers

OK so for every gram it is 1,000 mg so the answer to your question will be for 6,000 mg it will be 6 grams.

(1 point) For the equation given below, evaluate ′ at the point (−1,2). (5−)^4+4^3=2433. ′ at (−1,2) =

Answers

Answer:

$(343)/(71)$

Step-by-step explanation:

Given the equation

$(5x-y)^4+4y^3=2433$

Find the derivative:

$((5x-y)^4+4y^3)'=(2433)'\n \n4(5x-y)^3\cdot (5x-y)'+4\cdot 3y^2\cdot y'=0\n \n4(5x-y)^3\cdot (5-y')+12y^2y'=0$

Substitute

$x=-1\n \ny=2,$

then

$4(5\cdot (-1)-2)^3\cdot (5-y')+12\cdot 2^2\cdot y'=0\n \n4(-5-2)^3(5-y')+48y'=0\n \n4\cdot (-7)^3\cdot (5-y')+48y'=0\n \n-1,372(5-y')+48y'=0\n \n-6,860+1,372y'+48y'=0\n \n1,420y'=6,860\n \ny'=(6,860)/(1,420)=(686)/(142)=(343)/(71)$

In a city known for many tech start-ups, 311 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. In another city known for biotech firms, 334 of 800 randomly selected college graduates with outstanding student loans currently owe more than $50,000. Perform a two-proportion hypothesis test to determine whether there is a difference in the proportions of college graduates with outstanding student loans who currently owe more than $50,000 in these two cities. Use α=0.05. Assume that the samples are random and independent. Let the first city correspond to sample 1 and the second city correspond to sample 2. For this test: H0:p1=p2; Ha:p1≠p2, which is a two-tailed test. The test results are: z≈−1.17 , p-value is approximately 0.242

Answers

Answer:

Null hypothesis: $p_(1) - p_(2)=0$

Alternative hypothesis: $p_(1) - p_(2) \neq 0$

$z=\frac{0.389-0.418}{\sqrt{0.403(1-0.403)((1)/(800)+(1)/(800))}}=-1.182$

$p_v =2*P(Z<-1.182)=0.2372$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant difference between the two proportions.

Step-by-step explanation:

1) Data given and notation

$X_(1)=311$ represent the number college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$X_(2)=334$ represent the number college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)

$n_(1)=800$ sample 1

$n_(2)=800$ sample 2

$p_(1)=(311)/(800)=0.389$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 (tech start-ups)

$p_(2)=(334)/(800)=0.418$ represent the proportion of college graduates with outstanding student loans currently owe more than $50,000 ( biotech firms)