If f(x) = 3x³ + 5x² - 4, then what is the remainder when f(x) is divided by
x-1?

Answer: -1

Step-by-step explanation: 6x-12=-18

                                                 +12= +12

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

                                                     -6/6=-1

Expression of logarithms is log₅a³b = 3log₅a + log₅b.

Given expression is log₅a³b.

We have to express given expression as a sum or difference of logarithms.

We know the logarithmic formulas which is,

logₐ(PQ) = logₐP + logₐQ

logₐ([tex]P^{Q}[/tex]) = QlogₐP

we will use above formulas and solve the given equation.

log₅a³b = log₅a³ + log₅b

log₅a³b = 3log₅a + log₅b

Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.

The product property states that to miltiply two powers that have the same base, add the exponents.

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By solving a linear equation, it can be calculated that-

Kenji needs 12 gallons of gas for the drive

What is a linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Kenji requires x gallons of gas

Kenji's car gets 33.5 miles per gallon of gas when he is driving on the highway.

Kenji can travel 33.5x miles with x gallons of gas

Distance to be travelled = 402 miles

By the problem,

The required linear equation is

33.5x = 402

x = [tex]\frac{402}{33.5}[/tex]

x = 12 gallons

Kenji needs 12 gallons of gas for the drive

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Answer:

3, 8, 15 and 120

Step-by-step explanation:

to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule

n = 1 : 1² + 2(1) = 1 + 2 = 3

n = 2 : 2² + 2(2) = 4 + 4 = 8

n = 3 : 3² + 2(3) = 9 + 6 = 15

the first 3 terms are 3, 8, 15

to find the 10th term , substitute n = 10 into the rule

n = 10 : 10² + 2(10) = 100 + 20 = 120

The slope of a function is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.

m = Δy/Δx

∆y --> net change in the y coordinate

∆x ---> net change in x coordinate

m ---> slope of fution

The y-intercept of both functions 'f' and 'g' are equal and slope of f(x) is less than the slope of g(x). So, the correct option is option (A).

We have given a function, g (x) = 2x + 1

comparing the g(x) with standard equation

y = mx + b

where m is slope of this line

b --> y-intercept

Thus we get m = 2 , b= 1 . So, the slope of g(x) is 2 and y-intersecpt is 1 .

Now, we have a table for function f(x) that is function f(x) passing through all points as given in table. The slope of function passing through (h,k) and (a,b) is expressed as (k-b)/(h-a)

Thus, slope of function 'f' passing through (0,1) and (2,4) = (1-4)/(0-2) = -3/-2

= 3/2

=> f (x) = (3/2)x + b

where , b --> y-intercept

plug the value x= 4 and corresponding to it

f(x) = 7 we get , 7 = 3/2× 4 + b

=> b = 7-6 = 1

Therefore, slope of function g(x) is greater than slope of function f(x) and y-intercept of f(x) is equal to y-intercept g(x) .

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Complete question:

The Table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

x / f(x)

0/1

2/4

4/7

g(x)= 2x+1

A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

The probability is it that someone will correctly guess an 8-digit entry code is 0.022.

Given that,

A keypad with 10 buttons marked 0 through 9 is located at the building's entrance.

We have to find how much probability is it that someone will correctly guess an 8-digit entry code.

We know that,

Probability is defined as the ratio of the number of required outcomes to the total number of outcomes.

Based on the details provided;

One outcome is expected if the needed number of outcomes is 8-digits.

Since there are 10 numbers and 8 numbers need to be chosen, the total number of outcomes is ¹⁰C₈.

Considering that the lock can only be opened by 8 digits;

The probability that someone will properly guess a 8-digit input code is

P=1/¹⁰C₈

P=1/10!/8!2!

P=1/10×9/2

P=1/45

P=0.022

Therefore, The probability is it that someone will correctly guess an 8-digit entry code is 0.022.

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well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.

now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.

[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]

Answer: It means that the high in Dubai is 49

Step-by-step explanation: When saying about the weather, we always say the highest temperature first, so that mean 49 here is the high temperature in Dubai.

If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!

Answer:

The mercury is expected to cross the 49°C mark again later today.

Option-C is correct that is increase, wider. If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.

Given that,

By completing the blanks, the sentence is complete. When generating a confidence interval, the margin of error and the confidence interval will be larger if the level of confidence grows.

We have to find the accuracy of the confidence interval will increase with a larger sample size, so the margin of error and the confidence interval will be-----.

We know that,

If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.

The margin of error is a phrase that conveys how much sampling error there is in the data that was gathered or in the parameter estimates. Accordingly, the credibility of the poll will decrease as the margin of error increases. It displays the degree of estimation accuracy.

Three things determine the margin of error:

Confidence level: The margin of error grows in proportion to the level of confidence.

Sample size: The margin of error gets smaller as the size of the random sample gets bigger.

Population standard deviation: The population's standard deviation is: For a given level of confidence, our interval will be wider the more dispersed the population is.

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Answer: the first 1

Step-by-step explanation:

i just did it hope it helps

The no. of people qualified is less than the  managers belief of 0.265

What is P-value?

The likelihood of receiving outcomes from a statistical hypothesis test that are at least as severe as the actual results provided the null hypothesis is true, is known as the p-value in statistics. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.

P-value is frequently utilised by government organisations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.

Here [tex]H_{0}[/tex] - P =1/3=0.3333

Hi - P <0.3333

Given n =144

x = 63

P^=63/144=0.4375

Test Static = [tex]\frac{P^-P}{\sqrt{\frac{PQ}{n} } }[/tex]

= [tex]\frac{0.4375^-0.3333}{\sqrt{\frac{0.3333-(1-0.3333)}{144} } }[/tex]

=0.265

P-value =P(Z<2.65)=0.9960, Given [tex]\alpha[/tex] =0.05

here P-Value >[tex]\alpha[/tex]

So, don't reject  [tex]H_{0}[/tex]

There is no evidence to support the manager's Belief That less Than 1/3 of Applications are qualified

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Using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.

So, given that we've done it:

There are 35 players.

There are two coaches.

The cloth on the headbands measures 598.66 inches in length.

Just for the players, the wristbands include 302.05 inches of fabric.

Each player's headband's fabric length is specified by:

= Total inches/Total number of persons

= 598.66/37

= 16.18 inches

Each player's wristband's fabric length is specified by:

= Total inches/Number of persons

= 302.05/35

= 8.63 inches

Therefore, using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.

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Complete question:

Nancy is making accessories for the soccer team. She uses 598.66 inches of fabric on headbands for 35 players and 2 coaches. She also uses 302.05 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

The additional piece of information that is needed to show that the quadrilateral is a rhombus is given as follows:

The angle measures.

A rhombus is a quadrilateral, and is a special case of a parallelogram.

For the parallelogram to represent a rhombus, these following conditions need to be respected:

To verify if two sides are parallel, we need to verify their slopes, which are dependent on their angle measures. Hence these angle measures are the missing piece of information to define if the quadrilateral is a rhombus.

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Answer: (3,0)

Hope this helps! :)

Step-by-step explanation: Think of graphing, like regular number lines. The numbers are either positive or negative and depending on the integer you add or subtract, the number on the line will either move left or right.

x= 5 (x on a coordinate plane is left to right)

2 units left

5-2=3

y= -5 (y on a coordinate plane is top to bottom)

5 units up

-5+5=0

(3,0)

Answer:

(3,0)

Step-by-step explanation:

x= 5-2 = 3

y= -5+5 =0

Answer:

  y = 120°

Step-by-step explanation:

Given a triangle with external angle y and remote internal angles 33° and 87°, you want the measure of y.

The external angle is the sum of the remote internal angles:

  y = 33° +87°

  y = 120°

__

Additional comment

Angle x is supplementary to y, so its measure is ...

  x = 180° -y = 180° -120°

  x = 60°

Hopefully, you notice that the value of x is ...

  x = 180° -(33° +87°)

This is the same value you get when you solve the equation for the sum of angles in the triangle:

  33° +87° +x = 180°

Effectively, the rule regarding the external angle being the sum of remote internal angles is another way of saying the sum of angles in a triangle is 180°.

The value of c after solving the equation is 8.

For the polynomial to be divisible by x+2, hence x = -2

Given

p(x) = 4x³+cx²+x+2

p(-2) = 4(-2)³+c(-2)²+(-2)+2

p(-2) = 4(-8) + c(4)-2+2

p(-2) = -32+4c

If p(-2) = 0

0= -32+4c

-4c = -32

c = 32/4

c = 8

Hence we get the value of c as 8.

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When we do a confidence interval for the mean, we use T-distribution to determine the number of standard deviations needed for our confidence

The T-distribution is a way to describe a collection of observations in which the majority of the observations are close to the mean and the remaining observations are the tails on either side. It is a type of normal distribution that is utilized for data with unknown variance and smaller sample sizes.

We use the T-distribution to obtain the required critical value, which is nothing more than the number of standard deviations from the center taken to obtain the confidence interval, despite the fact that there is no population standard deviation and only sample metrics—the sample mean and standard deviation—are used. As a result, the solution to this problem is T-distribution.

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Answer: 2

Step-by-step explanation:

Since both triangles are similar you can set both side lengths to be equal

4x = 16x -24

Isolate x on one side

-12x = -24

Then solve for x

x = 2

Answer:78 feet and 34 cubic feet

Step-by-step explanation:

The last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.

Given that,

Each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it. For instance, the seventh term, which is the sum of the fifth ($8) and sixth ($32) terms, is $256. Though the numbers very rapidly become large, this series can go on indefinitely! In terms of the number of particles in the observable universe, the $14 term, for instance, is close to some estimations.

We have to find what is the final digit of the sequence's $35 term.

We know that,

Remember the Fibonacci sequence, which goes 1, 1, 2, 3, 5, 8, 13, 21..., where each word is the total of the one before it. Continuing the above pattern, if Fn is the n-th Fibonacci number, we would arrive at

aₙ=a₂ˣₙ₋₁a₁ˣₙ₋₂=2ˣₙ₋₁

A periodic series of residues mod 10 is left behind by the sequence of positive powers of 2:

2≡2(mod 10)

2²≡4 (mod 10)

2³≡8 (mod 10)

2⁴≡16 (mod 10)

2⁵≡32 (mod 10)

2⁶≡64 (mod 10)

And so forth; this series of residues has a 4-year period.

The taken mod 4 period is 6:

34≡4 (mod 6)

F₃₄≡3 (mod6)

2³=8

So, the last digit of a₃₅ is 8.

Therefore, the last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

sus

It will take about 16.7 years to reach $15500.

The percentage that a lender adds to the amount of money lent to them is called an interest rate.

Given that, the initial deposited amount is P = $15000, the interest rate is r= 0.2% annually, and the final amount is $15500.

The interest earned is calculated by subtracting the initial amount from the final amount:

15500-15000

=500

Therefore, the interest earned is $500.

Now, the formula for the simple interest is:

interest = P × r × t

Substitute the known values:

500 = 15000 × 0.2% × t

500 = 15000 × 0.2/100 ×t

500 = 30t

t = 500/30

t = 16.7

Hence, It will take about 16.7 years to reach $15500.

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Answer:

-3/7 > b

Step-by-step explanation:

subtract 5/7 on both sides

Answer: 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

116

Answer:

y=-4x+9

Step-by-step explanation:

We will find an equation in the form of y = mx + b. We know m must be -4(because the slope must be the same for parallel lines), so we need to solve for b, which is the y-intercept. To do that, we will plug in the point C, giving us [tex]5 = -4 * 1 + b[/tex]. Adding 4 to both sides gives us b = 9, so that is the y-intercept.

Answer:

The answer is x=20

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

(x+21)+(2x+9)=90

x + 21 + 2x + 9 = 90

combine numbers on left side:

x + 30 + 2x = 90

combine x terms on left side:

3x + 30 = 90

subtract 30 from both sides:

3x + 30 -30 = 90 - 30

3x  = 60

divide  both sides by 3:

3x/3  = 60/3

x = 20

The likelihood that a shooter will hit the target at least 13 times is 27.92%.

For such a binomial distribution, the probability density function equals the amount of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of achievements is five (i.e., x = 13), as we are keen in the development that the objective will be hit exactly five times.

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit the target at most 13 times.

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The probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week is 0.7224. Hence option C is the correct option.

What is the binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

The formula for z-score is z = (x -μ)/σ

Where, μ is mean of the sample, σ is standard deviation of the sample

Given that 55% of the customers buy coffee, hence p = 55% = 0.55

Sample of 35 customers, hence n = 35.

For the binomial distribution μ = np, σ = √[np(1-p)]

The mean and the standard deviation of the approximation are:

μ = 35 ˣ 0.55 = 19.25

σ = √[35 ˣ 0.55(1-0.55)] =2.943

Now calculate the z score where μ = 19.25, σ = 2.943 and X = 21

z = (21 -19.25)/2.943

z = 0.59

The value of p is 0.2776 when z score is 0.59.

The probability is 1 - 0.2776 = 0.7224.

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Answer:

false

Step-by-step explanation:

Hope it helps!

The measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

Applying intersecting secants theorem:

4(4 + 2) = 3(3 + 2x + 5)

8 = 8 + 2x

x = 0

LK = 2x + 5 = 5 units

In the second circle:

4(4 + x - 8) = 3(3 + x - 5)

x = 10

NL = x - 8 + 4 = 10 - 8 + 4 = 6 units

Thus, the measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.

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