To the nearest 10 thousand

Answer:

(First answer option)

Step-by-step explanation:

General form of an exponential function

\(y=ab^x+c\)

where:

Given exponential function:

\(y=4(10)^x-3\)

The x-intercept is the point at which the curve crosses the x-axis, so when y = 0.  To find the x-intercept, substitute y = 0 into the given equation and solve for x:

\(\begin{aligned}& \textsf{Set the function to zero}:& 4(10)^x-3 &=0\\\\& \textsf{Add 3 to both sides}:& 4(10)^x &=3\\\\& \textsf{Divide both sides by 4}:& 10^x &=\dfrac{3}{4}\\\\& \textsf{Take natural logs of both sides}:& \ln 10^x &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Apply the power log law}:&x \ln 10 &=\ln\left(\dfrac{3}{4}\right)\\\\& \textsf{Divide both sides by }\ln 10:&x&=\dfrac{\ln\left(\dfrac{3}{4}\right)}{\ln 10} \\\\& \textsf{Simplify}:&x&=-0.1\:\:\sf(1\:d.p.)\end{aligned}\)

Therefore, the x-intercept is (-0.1, 0) to the nearest tenth.

An asymptote is a line that the curve gets infinitely close to, but never touches.

The parent function of an exponential function is:

\(f(x)=b^x\)

As x approaches -∞ the function f(x) approaches zero, and as x approaches ∞ the function f(x) approaches ∞.

Therefore, there is a horizontal asymptote at y = 0.

This means that a function in the form  \(f(x) = ab^x+c\) always has a horizontal asymptote at y = c.  

Therefore, the horizontal asymptote of the given function is y = -3.

A graph representing exponential growth will have a curve that shows an increase in y as x increases.

A graph representing exponential decay will have a curve that shows a decrease in y as x increases.

The part of an exponential function that shows the growth/decay factor is the base (b).  

The base of the given function is 10 and so this confirms that the function is increasing since 10 > 1.

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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Answer:

Step-by-step explanation:

The true statements more or less speak for themselves.

The only value that has the same log for different bases is log(1) = 0 = ln(1). This means the first statement (A) is false.

The inverse function of y = e^x is found by swapping x and y:

  x = e^y

Taking natural logs of this equation gives you ...

  ln(x) = y

Hence the equations of B are, in fact, inverses.

Statement D is true, rendering statement C false.

The expressions in statement E are, in fact, equivalent, rendering E false.

Statement F shows the meaning of ln( ).

Statement G is a restatement of B. If two functions are inverses, their composition is x, the original argument.

The true statements are B, D, F, G.

__

The relevant rules of logarithms are ...

  log(a^b) = b·log(a)

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

Using these rules on the given expression, we have ...

  ln(x^4y/z) = ln(x^4y) -ln(z) = ln(x^4) +ln(y) -ln(z)

  = 4ln(x) +ln(y) -ln(z) . . . . . matches choice D

Answer:

43.6 has 3 significant figures.

Answer:

x = 49

Step-by-step explanation:

The sum of angles is 360

(x + 84) + 80 + 3x = 360

x + 3x = 360 - 84 - 80

4x = 196

x = 196/4 = 49

Answer:

c+c+c+c+50+5

Step-by-step explanation:

Answer/Step-by-step explanation:

Area of circle, A = πr²

Circumference of circle, C = 2πr or πd

1. r = 14 in.

A = π*14² = 615.75 = 615.8 in.² (nearest tenth)

C = 2*π*14 = 87.96 = 87.0 in (nearest tenth)

2. r = ½(16) = 8 ft

A = π*8² = 201.06 = 201.1 ft² (nearest tenth)

C = 2*π*8 = 50.27 = 50.3 ft (nearest tenth)

3. r = 1.7 cm

A = π*1.7² = 9.08 = 9.1 cm² (nearest tenth)

C = 2*π*1.7 = 10.68 = 10.7 cm (nearest tenth)

4. r = ½(13) = 6.5 m

A = π*6.5² = 132.73 = 132.7 m² (nearest tenth)

C = 2*π*6.5 = 40.84 = 40.8 m (nearest tenth)

Answer:

$22.00

Step-by-step explanation:

sales price x .05 = $1.90

Sales price = $1.90/.05

sales price = $38.00

total sales price less price of gloves = price of scarf

$38.00 - $16.00 = $22.00

Answer: (1,-2)

Step-by-step explanation:

To check which of the given ordered pairs satisfy the given system of nonlinear inequalities, we will substitute the values of x and y from each ordered pair and then check if the inequalities hold true or not. Let's check one by one.

For the ordered pair (1,-2):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (-2)

7 ≤ 25 + 2

7 ≤ 27 (This is true)

2 ≤ -y

2 ≤ -(-2)

2 ≤ 2 (This is true)

Therefore, (1,-2) satisfies the given system of nonlinear inequalities.

For the ordered pair (1,-3):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (-3)

7 ≤ 28 (This is true)

2 ≤ -y

2 ≤ -(-3)

2 ≤ 3 (This is true)

Therefore, (1,-3) does not satisfy the given system of nonlinear inequalities.

For the ordered pair (1,0):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (0)

7 ≤ 25 (This is true)

2 ≤ -y

2 ≤ -(0)

2 ≤ 0 (This is not true)

Therefore, (1,0) does not satisfy the given system of nonlinear inequalities.

For the ordered pair (0,0):

We do not have the value of x for this ordered pair, so we cannot check whether it satisfies the given system of nonlinear inequalities.

Hence, the ordered pair that satisfies the given system of nonlinear inequalities is (1,-2).

The values under and inside the radical is 4 and 129 respectively

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler.

A quadratic equation is given as ax²+ bx+ c=0

this can be solved using formula x=( -b±√b²-4ac)/2a.

in the equation 2x²-10=7x, it can be Rearranged As 2x²-7x-10= 0

a= 2, b= -7 and c= -10

x= -(-7)±√(-7)²-4×2×-10)/2×2

x= 7±√49+80)/4

x= 7/4 ± √129/4

therefore the values inside and under the radical is 129 and 4

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Answer:

C

Step-by-step explanation:

the answer is C

12*8=96

15*8=120

17*8=136

Answer:

2500 feet = 1 minute

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

24 - 7x = 10

Rearrange terms,

-7x + 24 = 10

Subtract 24 from both sides,

-7x + 24 - 24 = 10 - 24

-7x = 10 - 24

-7x = -14

Divide by sides by -7,

\(\frac{-7x}{-7}=\frac{-14}{-7}\)

\(x=\frac{-14}{-7}\)

x = 2

Answer: 6 ≤ x ≤ 11

Step-by-step explanation:

Let x be the number of additional outfits that can be packed in the suitcase.

The suitcase will fit at most 11 outfits, which means that x cannot be greater than 11 outfits.

On the other hand, 5 outfits have already been packed, so the number of additional outfits that can be packed is at least 6.

Therefore, the inequality that represents this situation is 6 ≤ x ≤ 11.

Answer:

£225

Step-by-step explanation:

[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]

100 + 25 = 125%

\(\frac{125}{100}\) × 180 = £225

It was stated that there were two possibilities during the day, that is, it can either be a sunny day or a rainy day.

Let us represent a sunny day with S, and represent a rainy day with R.

Using this to get the sample space for the three days as shown below

So, The total sample space is

The probability that it is sunny all three days would be

The Sample space for all sunny day is SSS. so number of element of all sunny day would be

Therefore, the probability that it is sunny all three days would be

Hence, the probability that it is sunny all three days is 1/8 or 0.125

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Answer:

10h = 370

hope this helps.

\(Question\)

How to put 399,005 in exponded from?

Answer:

300,000 + 99,000 + 5 + 0=

Hope this helps!

\(xXxAnimexXx\)

Given the points:

(x1, y1) ==> (1, 1)

(x2, y2) ==> (3, 7)

To find an equation of the line that goes through the points, first find the slope using the slope formula below:

Substitue values into the formula and solve for the slope, m:

The slope of the line, m is = 3.

Now, use the point slope form:

(y - y1) = m(x - x1)

Substitute 1 for y1, 1 for x1, and 3 for m:

(y - 1) = 3(x - 1)

Let's rewrite the equation to slope intercept form: y = mx + b

Where m is the slope and b is the y-intercept

y - 1 = 3(x) + 3(-1)

y - 1 = 3x - 3

Add 1 to both sides:

y - 1 + 1 = 3x - 3 + 1

y + 0 = 3x - 2

y = 3x - 2

Therefore, the equation of the line in slope intercept form is:

y = 3x - 2

ANSWER:

y = 3x - 2

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The statements that are true are B and D.

Given are some statements we need to check which is true.

Let's analyze each statement:

A. 4 is a perfect cube.

False. 4 is not a perfect cube because there is no integer that can be cubed to give 4.

B. 16 is a perfect square.

True. 16 is a perfect square because it can be expressed as 4^2, where 4 is an integer.

C. 2,197 is both a perfect square and a perfect cube.

False. 2,197 is not a perfect square because there is no integer that can be squared to give 2,197.

However, it is a perfect cube because 13³ equals 2,197.

D. 8 is a perfect cube.

True. 8 is a perfect cube because it can be expressed as 2³, where 2 is an integer.

E. 18 is neither a perfect square nor a perfect cube.

True. 18 is neither a perfect square nor a perfect cube because there is no integer that can be squared or cubed to give 18.

Therefore, the statements that are true are B and D.

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Answer:

y = 3

x = 2

Step-by-step explanation:

-5x + 4y = 2

9x - 4y = 6

Sum both eq.

-5x + 9x = 4x

+4y - 4y = 0

2 + 6 = 8

then:

4x + 0 = 8

4x = 8

x = 8/4

x = 2

from the first eq.

-5x + 4y = 2

-5*2 + 4y = 2

-10 + 4y = 2

4y = 2 + 10

4y = 12

y = 12/4

y = 3

Check:

from the second eq.

9x - 4y = 6

9*2 - 4*3 = 6

18 - 12 = 6

The Average distance from point in a ball of radius 4 to the center as a triple integral is ⇒ 1/(4/3 * π *4³)× \(\int\limits^{2\pi }_0 \int\limits^{\pi }_0 \int\limits^4_0 {\rho.{\rho}^{2} } \, sin\phi .d\rho .d\phi .d\theta\)   and the average distance is 3 units .

In the question ,

it is given that ,

the radius of the ball is 4 ,

that means ρ = 4 .

So , using spherical coordinates ;

the region is given by

E = {(ρ,Φ,θ) | 0≤ρ≤4 , 0≤Φ≤π , 0≤θ≤2π }

So , the triple integral representation of the  average distance is given by

AD = (∫∫∫d(x,y,z) dV)/(∫∫∫1 dV)

= 1/(4/3 * π *4³)× \(\int\limits^{2\pi }_0 \int\limits^{\pi }_0 \int\limits^4_0 {\rho.{\rho}^{2} } \, sin\phi .d\rho .d\phi .d\theta\)

= 1/(4/3 * π *4³) × \(\int\limits^{2\pi }_0 \int\limits^{\pi }_0 \int\limits^4_0 {{\rho}^{3} } \, sin\phi .d\rho .d\phi .d\theta\)

Integrating further ,

we get ;

= (3/256π) × \(\int\limits^{2\pi }_0\int\limits^{\pi }_0\)[ρ⁴/4]⁴₀ sinФ.dФ.dθ

Simplifying further ,

we get ,

= 3/4π × 2 × [θ] 2π to 0

= (3/2π) × 2π

= 3

Therefore , the Average distance is 3 units .

The given question is incomplete , the complete question is

Express the the average distance from a point in a ball of radius 4 to its center as a triple integral and evaluate it .

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The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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Answer: 210 dollars left.

Happy to Help :)

Step-by-step explanation:

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²