27
A radioactive substance decays at an annual rate of
13 percent. If the initial amount of the substance is
325 grams, which of the following functions i
models the remaining amount of the substance. In
grams, 1 years later?
A) f(t) = 325(0.877'
B) f(t) = 325(0.13)
C) f(t) = 0.87(325)
D) (t) = 0.13(325)

Answer:

14/9 inches, or an inch and 5/9 of an inch.

Step-by-step explanation:

If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.

[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]

9 * x = (2/3) * 21

9x = 2 * 7

9x = 14

x = 14/9 inches.

Hope this helps!

Answer:

1 5/9 ich represent 21 miles

Step-by-step explanation:

Proportions:

2/3  inch  ⇔   9 miles

M  inch   ⇔    21 miles

M = 21*(2/3) / 9

M = 14/9

14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch

Answer:

Step-by-step explanation:

If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is

[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:

[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to

[tex]8x=-y^2[/tex] and, solving for x:

[tex]x=-\frac{1}{8}y^2[/tex]

Answer:

6.87 g/mL

Step-by-step explanation:

The density of an object can be found by dividing the mass by the volume.

[tex]density=\frac{mass}{volume}\\\\ d=\frac{m}{ v}[/tex]

We know that the aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. Therefore, the mass is 87.3 g and the volume is 12.7 mL.

[tex]m= 87.3 g\\\\v=12.7 mL[/tex]

Substitute the values into the formula.

[tex]d= \frac{87.3 g}{12.7 mL}[/tex]

Divide 87.3 g by 12.7 mL

[tex]d=6.87401575 g/mL[/tex]

Round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.

[tex]d= 6.87 g/mL[/tex]

The density of the aluminum is about 6.87 grams per milliliter.

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

Answer:

18.18 min

Step-by-step explanation:

The complete question is

On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?

The initial temperature of the engine [tex]T_{1}[/tex] = -18 F

rate of increase in temperature r = 5.4 F/min

Final temperature [tex]T_{2}[/tex]  = 80 F

Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F

time taken to reach this 80 F will be = ΔT/r

where ΔT is the difference in temperature

r is the rate of change of temperature

time taken = 98/5.4 = 18.18 min

Answer:

Hey there!

The temperature started at -8 degrees.

The total rise of the temperature was 6(4) or 24 degrees.

-8+24=16

The temperature after 6 hours was 16 degrees.

Let me know if this helps :)

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.

Given that, One January day, the low temperature in Fargo, ND was -8 degrees.

Over a period of six hours, the temperature rose 4 degrees per hour.

So, total temperature rose in 6 hours is 24 degrees

Temperature after 6 hour is -8+24

= 16°

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

Learn more about the temperature here:

https://brainly.com/question/11464844.

#SPJ2

Answer:

dL/dt  = - 2,019 m/h

Step-by-step explanation:

L²  =  x²  +  y²   (1)    Where  x, and  y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then  dx/dt =  2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt  + 2*y*dy/dt

L*dL/dt  = x*dx/dt + y*dy/dt         (2)

When  the base is 9  and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)²       ⇒    L = √565       ⇒  L  = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt  = x*dx/dt + y*dy/dt

23,77 * dL/dt  = 9*2 + 22* ( - 3)

dL/dt  =  ( 18 - 66 ) / 23,77

dL/dt  = - 2,019 m/h

Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.

The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:

[tex]h^2 = x^2 + y^2[/tex]

In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:

[tex]h^2 = 9^2 + 22^2[/tex]

[tex]h = \sqrt{9^2 + 22^2}[/tex]

[tex]h = 23.77[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Simplifying by 2:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].

We want to find [tex]\frac{dh}{dt}[/tex], hence:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]

[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]

[tex]\frac{dh}{dt} = -2.02[/tex]

The hypotenuse is changing at a rate of -2.02 meters per hour.

A similar problem is given at https://brainly.com/question/19954153

Answer:

The answer to the nearest hundredth is 0.07 liters per minute

Step-by-step explanation:

In this question, we are told to express the given metric in liters per minute.

The key to answering this question, is to

have the given measurements in the metric in which we want to have the answer.

Hence, we do this by converting milliliters to liters and seconds to minute.

Let’s start with milliliters;

Mathematically;

1000 milliliters = 1 liters

10 milliliters = x liters

x * 1000 = 10 * 1

x = 10/1000

x = 1/100

x = 0.01 liters

For the seconds;

We need to convert the seconds to minutes;

Mathematically;

60 seconds = 1 minute

8.5 seconds = y minutes

60 * y = 8.5 * 1

y = 8.5/60

y = 0.14167 minutes

Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;

Hence, we have ;

0.01/0.14167 = 0.070588235294

Which to the nearest hundredth is 0.07

Answer:

78 nickels and 22 dimes

Step-by-step explanation:

Nickels = n, Dimes = d

Number of coins = 100

Total sum in the piggy bank = $6.60

Consider the first equation in the second:

Answer: nickels 78 and dimes 22

Answer:

78 nikes and dimes 22

solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11

Step-by-step explanation:

Answer:

=2x+3/4=5.50

x=19/8 or 2 3/8

hope this helps

Step-by-step explanation:

Answer:

1 3/4 cups is between the 13th and 15th lines from the bottom.

Step-by-step explanation:

The bottom of the cup has no line and corresponds to 0 eights.

1st line up: 1/8 cup  

2nd line up: 2/8 cup    this is also called 1/4 cup

3rd line up: 3/8 cup

4th line up: 4/8 cup     this is also called 1/2 cup

5th line up: 5/8 cup

6th line up: 6/8 cup     this is also called 3/4 cup

7th line up: 7/8 cup

8th line up: 8/8 cup     this is also called 1 cup

9th line up: 9/8 cup

10th line up: 10/8 cup    this is also called 1 1/4 cup

11th line up: 1 3/8 cup

12th line up: 1 4/8 cup     this is also called 1 1/2 cup

13th line up: 1 5/8 cup

14th line up: 1 6/8 cup    this is also called 1 3/4 cup

15th line up: 1 7/8 cup

16th line up: 1 8/8 cup    this is also called 2 cups

1 3/4 cups is between the 13th and 15th lines from the bottom.

Answer:

1 mile/hour is equivalent to 1.47 feet/seconds

Step-by-step explanation:

Given

[tex]88 ft/s= 60 miles/hr[/tex]

Required

Determine the equivalent of 1 mile/hour

[tex]88\ ft/s= 60\ miles/hr[/tex]

Express 60 as 60 * 1

[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]

Divide both sides by 60

[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]

[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]

Reorder

[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]

Divide 88 by 60

[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]

Approximate to 3 significant figures

[tex]1\ mile/hr = 1.47\ ft/s[/tex]

Hence;

1 mile/hour is equivalent to 1.47 feet/seconds

Answer:  48

There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.

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

1 min = 60 sec

30 min = 1800 sec (multiply both sides by 30)

1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")

The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.

There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.

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

Extra info:

If you're curious about finding the more accurate value, then you could follow these steps

1 prize = 2014 seconds

x prizes = 86400 seconds (number of seconds in a full day)

1/x = 2014/86400

1*86400 = x*2014

86400 = 2014x

2014x = 86400

x = 86400/2014

x = 42.8997020854021

Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.

Answer:

p(x), q(x), and their product are all polynomials.

p(x) · q(x) = 6x² + 10x - 63

Step-by-step explanation:

First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.

process of multiplying

Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of

6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use cosine

cos∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 10

Substitute these values into the above formula and solve for x

That's

Divide both sides by cos 37

x = 12.52135

We have the final answer as

Hope this helps you

Answer:

probably 16.5

Step-by-step explanation:

Answer:

we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Step-by-step explanation:

From the given information;

Sample  size n = 12

the probability of passing a student who guesses on every question is less than 0.10

In a alternative - response question (true/false) question, the probability of answering  a question correctly  = 1/2 = 0.5

Let X be the random variable that is represent number of correct answers out of 12.

The X [tex]\sim[/tex] BInomial (12, 0.5)

The probability mass function :

[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]

[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]

P(X = 12) = 2.44 × 10⁻⁴

[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]

P(X =11 ) = 0.00293

[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]

P(X = 10) = 0.01611

[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]

P(X = 9) = 0.0537

[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]

P(X = 8)  = 0.12085

[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]

P(X = 7) = 0.19335

.........

We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01

As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Answer:

C. x-2

Step-by-step explanation:

edge

Answer: the 3rd the answer c

x-2

Step-by-step explanation:

Answer:

x= 24

Step-by-step explanation:

open the bracket

4×3x =12x + 4 × 2 =8

12×+ 8-6×6

12×+ 12

x= 24

Answer:

12x - 28

Step-by-step explanation:

Because of PEMDAS you start with the parentheses and distribute the 4.

So,

(12x + 8) -6 x 6

Then, solve for the 6's

(12x + 8) -36

Remove the parentheses

12x + 8 - 36

Lastly, you get

12x - 28.

This is as far as you can go because there is no equals sign so you cannot actually solve for x.

Answer:

x = 50

Step-by-step explanation:

Since the angle is right = 90°, then

40 + x = 90 ( subtract 40 from both sides )

x = 50

Answer:

[tex]\boxed{\sf x = 50\ degrees}[/tex]

Step-by-step explanation:

x = 90 - 40    [Complementary angles add up to 90 degrees]

x = 50 degrees

Answer:

Yes it will occur

Step-by-step explanation:

The lobby measures 45 feet by 45 feet

Area of the lobby = 45 * 45

=2025 ft^2

So, the lobby has 2025 tiles

subtract 1 black tile in the center

2025 tiles - 1 black tile =2024 tiles

The number of blue tiles and black tiles is 2024 tiles

He wants the outer edge to be the same color as the center tile so, divide by 2

2024/2 = 1012 tiles

The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles

Answer:

9, 13, 17, 21

Step-by-step explanation:

If x=2,

y=1+4(2)

y=9

This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

Answer:

We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Step-by-step explanation:

The complete question is: In a previous​ poll, ​46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose​ that, in a more recent​ poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.

Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.

So, Null Hypothesis, : p 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}

Alternate Hypothesis, : p < 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

                             T.S.  =    ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44

           n = sample of adults with children under the age of 18 = 1081

So, the test statistics =    

                                   =  -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)

                                  = 1 - 0.9066 = 0.0934

Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Answer:

$36,400

Step-by-step explanation:

Mr Jamison deposited $100 in January

February=3*100=$300

March=3{3(100)=3^2(100)=9*100=$900

April=3^3(100)=27*100=$2,700

May=3^4(100)=81*100=$8,100

June=3^5(100)=243*100=$24,300

Total amount=$100 + $300 + $900 + $2700 + $8100 + $24300

=$36,400

The total amount deposited by Mr Jamison on June 15 is $36,400

Answer:

$2 per pound = $0.125. per pound

Step-by-step explanation:

The unit of weight conversion from pound to ounce is given as follows;

1 pound weight  = 16 ounces weight

1 ounce weight = 1/16 pound weight

Therefore, whereby the cost of 1 pound weight of an item is two dollars, we have;

The cost of one ounce weight of the item will be the cost of 1 pound weight, divided by 16 and given as follows;

$2 per pound = $2/16 per pound  = $0.125. per pound

Therefore;

$2 per pound = $0.125. per pound.

Answer and Step-by-step explanation: The described right triangle is in the attachment.

As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:

AC² = AB² + BC²

[tex]AB^{2} = AC^{2}-BC^{2}[/tex]

[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]

[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]

[tex]AB =\sqrt{28.75}[/tex]

AB = 5.4

Then, right triangle ABC measures:

AB = 5.4cm

BC = 4.5cm

AC = 7cm

Answer:

13x3= 39

Step-by-step explanation:

10x3=30

3x3=9

30+9=39

Hope it helps!

Answer:

2040 miles

Step-by-step explanation

Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline

with this info we can find out how many gallons of gas Jose can buy.

81 divided by 1.35 is 60 gallons of gas

we also know that he can travel 34 miles for each gallon of gas

with this we can find out how far jose can travel

34 multiplied by 60 is 2040 miles

so, with $81, Jose can travel 2040 miles if gas prices are $1.35

Answer:

H. b/a

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Label our variables

y₂ = 2b

y₁ = b

x₂ = 2a

x₁ = a

Step 2: Plug into formula

m = (2b - b)/(2a - a)

Step 3: Evaluate

m = b/a

Answer:

b/a

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2b - b)/ ( 2a -a)

   = b/a