At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37.5 grams.




What is the half-life of the goo in minutes?


________



Find a formula for


G(t),


the amount of goo remaining at time T.


G= _________



How many grams of goo will remain after 32 minutes?

Answer:

True

Step-by-step explanation:

Answer:

C. F(x) = 4x² + 1

Step-by-step explanation:

→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.

→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.

This means the correct answer should be "C. F(x) = 4x² + 1."

Answer:

C.

Step-by-step explanation:

Base area = 9 × 13

= 117 square feet

Now

Volume of pyramid = (1/3)(A)(H)

= (1/3)(117)(30)

= 117 × 10

= 1170 cubic feet

Answer: you would need 776 yards to make both dresses

Step-by-step explanation:

You would need to find the sum of the amount if yards needed for both dresses.

The first dress needs 418 yards

The seconds dress needs 358 yards

418 + 358 = 776

Therefore you would need 776 yards to be able to make both of the dresses

Answer:

Null hypothesis is rejected,

test statistic= 15.76

Step-by-step explanation:

sample mean= 113,

sample standard deviation= 68

H0: mean of sample =100

Ha: mean of sample > 100

test statistic= (population mean- sample mean)/√(standard deviation/sample size)

test statistic= (113-100)/√(68/100)= 15.76

Degrees of freeedom= 100-1=99

p-value= 1.658 (from t distribution table for DF=99 and alpha=0.05)

Since p-value is smaller than test statistic, null hypothesis is rejected

Answer:

The nearest time is 15 years or 180 months

Answer:

c, Z

Step-by-step explanation:

x+y=4

y+z=5

y=4-x

4-x+z=5

-x+z=1

z=1+x

Answer:

a. Standard deviation: 4.082

Standard error: 2.041

b. The 95% confidence interval for the actual temperature is (298.5, 311.5).

Upper bound: 311.5

Lower bound: 298.5

c. Test statistic t=2.45

P-value = 0.092

d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.

e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.

This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.

Step-by-step explanation:

The mean and standard deviation of the sample are:

[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=305.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]

The 95% confidence interval for the actual temperature is (298.5, 311.5).

This is a hypothesis test for the population mean.

The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]

The significance level is 0.05.

The sample has a size n=4.

The sample mean is M=305.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]

As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.

Answer:

Step-by-step explanation:

BRUH YOU STUPID

Answer:

0

[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]

Answer: The answer is 61

Step-by-step explanation: did it on 2020 edg pls mark me brainliest

Answer:

61

Step-by-step explanation:

Answer:

Read below

Step-by-step explanation:

To graph the inequality, place an open circle on -2.5 because there is no line under the > sign. Draw the arrow pointing to the right because the inequality reads "x is greater than -2.5.

As for the check box questions, only B and C should be checked. The arrow points right, and the circle is open.

Answer:

5, yes.

Step-by-step explanation :

Answer:

D. $7.50

Step-by-step explanation:

$157.50 / 21 hours = $7.50 per hour

Answer:

Arc EF = 11.30

Step-by-step explanation:

For Circle A

S = r∅

18.08=(8)∅

Where ∅ is the angle subtended by the Arc

So

∅ = 18.08/8

∅ = 2.26 (in radians)

Now

For Circle C

S = r∅

S = (5)(2.26)

S = 11.30

Answer:

a) false

b) true

c) false

d) false

Step-by-step explanation:

a) p-value is compared with test statistic to either accept or ereject the null hypothesis. There is no fixed p-value to reject the null hypothesis

b) p-value tells us the probabiltiy of finding null hypothesis to be true

c) There is no fixed p-value for nullyfying the the null hypothesis

d) There is no fixed p-value to reject the null hypothesis

Answer:

a) 0.32 = 32% probability that your bid will be accepted

b) 0.72 = 72% probability that your bid will be accepted

c) An amount in excess of $15,400.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.

This means that [tex]a = 10400, b = 15400[/tex]

a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?

You will win if the competitor bids less than 12000. So

[tex]P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32[/tex]

0.32 = 32% probability that your bid will be accepted

b. Suppose you bid $14,000. What is the probability that your bid will be accepted?

You will win if the competitor bids less than 14000. So

[tex]P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72[/tex]

0.72 = 72% probability that your bid will be accepted

c. What amount should you bid to maximize the probability that you get the property (in dollars)?

His bid is uniformly distributed between $10,400 and $15,400.

So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.

Answer:

The total weight of his purchase is 1.08 pounds

Step-by-step explanation:

To find the total weight of his purchase, we sum the weight of each of his purchases.

He purchased:

4/9 pound of peanut.

7/11 pounds of raisins

Total:

The least common multiple between 9 and 11 is 99.

Then

[tex]\frac{4}{9} + \frac{7}{11} = \frac{11*4 + 9*7}{99} = \frac{107}{99} = 1.08[/tex]

The total weight of his purchase is 1.08 pounds

Answer:

[tex]f(theta)=sin(theta) - cos(theta)[/tex] + C

This is my first time doing a double integral, so im only 90% sure in my answer

Step-by-step explanation:

You pretty much want to take the double integral of sinx + cosx

The anti-derivative of sinx = -cosx

The anti-derivative of cosx = sinx

So f' = -cosx + sinx

Now lets take the integral of f':

The anti-derivative of -cosx = sinx

The anti-derivative of sinx = -cosx

So, f(x) = sinx - cosx

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

Work Shown:

I'll use x in place of theta since its easier to type on a keyboard.

f '' (x) = sin(x) + cos(x)

f ' (x) = -cos(x) + sin(x) + C ..... integrate both sides; dont forget the plus C

f ' (0) = 1

f ' (0) = -cos(0) + sin(0) + C

-cos(0) + sin(0) + C = 1

-1 + 0 + C = 1

C = 1+1

C = 2

So,

f ' (x) = -cos(x) + sin(x) + C

turns into

f ' (x) = -cos(x) + sin(x) + 2

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

Now integrate both sides of the first derivative to get the original f(x) function

f ' (x) = -cos(x) + sin(x) + 2

f(x) = -sin(x) - cos(x) + 2x + D .... apply integral; D is some constant

f(0) = -sin(0) - cos(0) + 2(0) + D

f(0) = 0 - 1 + 0 + D

f(0) = D - 1

f(0) = 2

D-1 = 2

D = 2+1

D = 3

We have f(x) = -sin(x) - cos(x) + 2x + D update to f(x) = -sin(x) - cos(x) + 2x + 3

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

So f '' (x) = sin(x) + cos(x) becomes f(x) = -sin(x) - cos(x) + 2x + 3 when f(0) = 2 and f ' (0) = 1

The last step is to replace every x with theta so that we get back to the original variable.

f(x) = -sin(x) - cos(x) + 2x + 3   turns into   f(θ) = -sin(θ) - cos(θ) + 2θ + 3

Answer:

4

Step-by-step explanation:

10-2(1)=8 which is >=4

10-2(2)=6 which is >=4

10-2(3)=4 which is >=4

10-2(4)=2 which isn't >=4

Therefore 4 doesn't satisfy the inequality

Answer:

4

Step-by-step explanation:

Let's test each possibility.

10-2(1)≥4

10-2=8 so it works

10-2(2)≥4

10-4=6 so it works

10-2(3)≥4

10-6=4 so it works

10-2(4)≥4

10-8=2

2<4 so it dosen't fit the solution

Answer:

d = 2

Step-by-step explanation:

Using the formula

A=pq/2

Dont forget to click THANKS

Answer:

D. 6.3

Step-by-step explanation:

Well you can make a triangle with the line PQ with it's height as 2 and base as 6.

Then you can use the Pythagorean Theorem to find the length of PQ.

a²+b²=c²

2²+6²=c²

4+36=c²

40=c²

c²=40

Square root both sides

c=[tex]\sqrt{40}[/tex]

c≈6.3

Our answer is D. 6.3

Answer:

[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]

Step-by-step explanation:

In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.

For a second order differential equation of type:

[tex]ay''+by'+cy=0[/tex]

Has characteristic equation:

[tex]a r^{2} +br+c=0[/tex]

Whose solutions [tex]r_1 , r_2 ,.., r_n[/tex] are the roots from which the general solution can be formed. There are three cases:

Real roots:

[tex]y(x)=c_1e^{r_1 x} +c_2e^{r_2 x}[/tex]

Repeated roots:

[tex]y(x)=c_1e^{r x} +c_1 xe^{r x}[/tex]

Complex roots:

[tex]y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i[/tex]

Therefore:

The characteristic equation for:

[tex]y''+6y'+13y=0[/tex]

Is:

[tex]r^{2} +6r+13=0[/tex]

Solving for [tex]r[/tex] :

[tex]r_1_,_2= -3 \pm 2i[/tex]

So:

[tex]\mu = 2\\\\and\\\\\lambda=-3[/tex]

Hence, the general solution of the differential equation will be given by:

[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]

Answer:

The number of computer is 5 and printer is 3

Answer:

Base of the Pennant = 330 pixels

Scale Factor =0.6

Step-by-step explanation:

The base measure of the pennant on screen is 550 pixels.

The height  is 275 pixels.

[tex]A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1[/tex]

If Charlotte resizes the pennant, keeping the aspect ratio  constant.

Height = 165 pixels

Therefore:

[tex]\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330[/tex]

Therefore, the scale factor of the dilation  [tex]=\dfrac{330}{550}= \dfrac{165}{275}=0.6[/tex]

Base of the Pennant = 330 pixels

Scale Factor =0.6

Answer: 62

Step-by-step explanation:

Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.

Hope that helped,

-sirswagger21

Answer:

Step-by-step explanation:

Area = area of rectangle 1 + area of rectangle 2 + area of rectangle 3 +area of triangle

= 8*12 +  12*9 + 19 *5 +  (1/2) * 4 *12

= 96 + 108 + 95 + 24

= 323 sq. cm

Answer: No

Step-by-step explanation:

Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.

Hope that helped,

-sirswagger21

Answer:24y

Step-by-step explanation:

Answer:

[tex]a^{\frac{9}{2}}[/tex]

Step-by-step explanation:

[tex]\left(a^{\frac{3}{2}}\right)^3[/tex]

[tex]=a^{\frac{3}{2}\cdot \:3}[/tex]

[tex]=a^{\frac{3}{2}\cdot \frac{3}{1}}[/tex]

[tex]=a^{\frac{9}{2}}[/tex]

Answer:

The length of the second line is [tex]9\frac{1}{15}[/tex] inches

Step-by-step explanation:

Given

Length of first line = [tex]6\frac{4}{10}[/tex] inches

Length of second line = [tex]2\frac{2}{3}[/tex] inches longer

Required

Length of second line.

Let the length of the second line be represented by x.

From the question, x is [tex]2\frac{2}{3}[/tex] inches longer than the first line;

This implies that:

[tex]x = 2\frac{2}{3} + 6\frac{4}{10}[/tex]

Convert both fractions to improper fractions

[tex]x = \frac{8}{3} + \frac{64}{10}[/tex]

Take LCM

[tex]x = \frac{80 + 192}{30}[/tex]

[tex]x = \frac{272}{30}[/tex]

Convert to mixed fraction

[tex]x = 9\frac{2}{30}[/tex]

Reduce fraction to lowest term

[tex]x = 9\frac{1}{15}[/tex]

Hence, the length of the second line is [tex]9\frac{1}{15}[/tex] inches