Given parallelogram DEFG, if DF = 5x + 1, what is XF?

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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The test statistic of two brands of batteries is -2.177.

[tex]n_1[/tex] = size of sample 1 = 16

[tex]n_2[/tex] = size of sample 2 = 21

[tex]\bar{x_1}[/tex] = mean of sample 1 = 210

[tex]\bar{x_2}[/tex] = mean of sample 2 = 225

[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20

[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23

T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,

t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]

t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]

t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]

t = -15 / 7.0845

t = -2.117

Thus, the two brands of batteries have test statistic result is -2.117

Your question is incomplete, but most probably your full question was

Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:

Sample 1: n1= 16, X1 = 210, s1= 20

Sample 2: n2= 21, X2 = 225, s2= 23

What is the test statistic assuming unequal population standard deviations?

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Answer:

0.3

Step-by-step explanation:

0.9 times 0.3 equals 0.27

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:

see explanation

Step-by-step explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 21 when x = 14 , then

21 = 14k ( divide both sides by 14 )

[tex]\frac{21}{14}[/tex] = k , that is

k = [tex]\frac{3}{2}[/tex] = 1.5

y = 1.5x ← equation of variation

when x = 40 , then

y = 1.5 × 40 = 60

Answer:

Step-by-step explanation:

domain = all real numbers

x-intercepts (2,0)

y-intercepts (0,-14)

vertex = minimum (-3/1 - 121/8)

Answer: Okay so I got,

1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)

2) 'x' equals to..

-Exact Form: 2, -7/2

-Decimal Form: 2, -3.5

Hope this helps!

The difference between these distances on the Earth is 3.32 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.

The difference will be:

= 4.00x10^4 km - 6.8x10^3 km.

= 3.32 × 10⁴

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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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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?

In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.

Regression analysis:

In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.

Given,

Here we need to find the type of variable for  a regression analysis, a(n) is used to predict a(n).

As per the definition of regression analysis, in the given question, we have two variable there are

=> a(n)

After prediction, the predicted value of a(n).

Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.

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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, 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

If we can notice the difference between 10- and 11-pound weight, we can  differentiate 110-pound weight from a 100-pound weight.

All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.

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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.

46 pounds of prepped cucumbers are needed for 140 house salads.

It is given that one cup of diced cucumbers weighs 5.3 ounces.

Also, we know that one pound= 16 ounces or 1-ounce measure 1/16 pounds, we can do it in any way.

Thus, firstly, we will convert the ounces into pounds.

thus, 5.3 ounces= 5.3/16 pounds

Now, we need prepped cucumbers for 140 house salads, According to the given question.

thus, pounds needed for 140 house salads= 5.3/16*140

=>  46 pounds (nearly)

Thus, 140 house salads need nearly 46 pounds of cucumbers.

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Answer:

false

Step-by-step explanation:

Hope it helps!

Answer:

Step-by-step explanation:

1. Square

2. Rhombus

3. Trapezoid

4. Diamond

5. Octogon

6. Triangle

7. Pentagon

8. Hexagon

9. Triangle?

The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.

Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).

When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;

When we rotate 180 degree counterclockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

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Answer: -1

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

                                                 +12= +12

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

                                                     -6/6=-1

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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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: the first 1

Step-by-step explanation:

i just did it hope it helps

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:

it would be CD or 50%

Step-by-step explanation:

Answer:

It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.

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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The sum of the indicated variable is 23.

What is variable?

A variable is an  alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.

MAIN body:

the correct expression is as follows :

1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!)   where m = 3

for m= 3

the expression becomes:

=1(1!) +2(2!) +3(3!)

factorial means we need to multiply the number until it reaches 1.

= 1*1 + 2*2*1 + 3*3*2*1

= 1+ 4+ 18

= 23

Hence the sum of expression is 23.

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Answer: 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

116