One day last summer, Tommy decided to take a drive into the countryside.

After a few hours' drive he arrived at a farm stand. Tommy was so excited by the sight of all those fresh fruits and veggies, that he tripped getting out of his MG and knocked over a huge basket of eggs. And of course they all broke!

He asked the farmer how many eggs were in the basket because he obviously wanted to compensate her for them. She said she didn't know exactly.

"But I do know,' she said, "that this morning I decided the eggs would be easier to sell if they weren't in a big basket but if they were in little paper bags.

"So when I took all my eggs and placed two in each bag I had one left over. I didn't like that so I took the eggs and I put three in each bag. And when I did that, I also had one left over.
"When I put four in each bag, I had one left over. When I put five in a bag or six in a bag, I had one left over. And when I put seven in a bag, I had none left over."


So here's the question: what's the smallest number of eggs that Tommy should have to pay for?

If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.

The rational zero theorem is used to determine the rational roots of a polynomial function.

Rational Zero Theorem statement:-

The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients

f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,

p is a factor of the constant a₀,

q  is a factor of the leading coefficient an,

and p and q are relatively prime.

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We can see here that the probability that the password does not have repeated letters, expressed to the nearest tenth of a percent is = 9.8%.

Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of an event can be calculated using the following formula:

Probability = Favorable Outcomes / Total Outcomes

The number of possible passwords is:

26 × 26 × 26 × 26 × 26 × 26  = 308,915,776.

The number of passwords with no repeated letters is

26P6 = 30,260,000.

The probability of a password having no repeated letters is

= 30,260,000 / 308,915,776 = 0.09779 = 9.78%.

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Answer:

0, -3

Step-by-step explanation:

Attachment.

In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.

Answer:

84

Step-by-step explanation:

To calculate how much 140% of 60 does we need to multiply 60 with 140 then divide it by 100

60 x 140 ÷ 100 = 84

Answer:

x = 26

Step-by-step explanation:

Answer:

○ \(\displaystyle y = 2x + 7\)

Step-by-step explanation:

Use the Slope-Intercept Formula instead of the Point-Slope Formula because it is MUCH, MUCH faster, plus parallel equations have SIMILAR RATE OF CHANGES [SLOPES ], so \(\displaystyle 2\) remains as is:

\(\displaystyle y =mx + b \\ \\ 3 = 2[-2] + b → 3 = -4 + b; 7 = b \\ \\ \boxed{y = 2x + 7}\)

I am joyous to assist you at any time.

In order to determine which equation represents the boundary, replace the values of the coordinates of the given points, into the choices for the equations, and then verify if the left hand side matches with the right hand side.

For points (35,0) and (5,0) you have:

x = 35

y = 0

x = 5

y = 0

Then, for the first answer choice we have:

As you can notice, the equation matches for values of x and y.

Then, there is no necessary to verify for the other choices.

Hence, the equation (x - 20)^2 + y^2 = 225 represents the boundary that the sprinkler covers.

The simplified expressiοn fοr |x + 3|, when x > 5, is simply |8 < x < ∞|.

In mathematics, an expressiοn οr mathematical expressiοn is a finite cοmbinatiοn οf symbοls that is well-fοrmed accοrding tο rules that depend οn the cοntext. Mathematical symbοls can represent numbers (cοnstants), variables, pertains, functiοns, brackets, punctuatiοn, and grοuping tο help determine the rder οf peratins and οther aspects οf lοgical syntax.

Many authοrs distinguish an expressiοn frοm a fοrmula, with the fοrmer denοting a mathematical object and the latter denοting a statement abοut mathematical objects.

If x > 5, then x + 3 is pοsitive, sο we can simplify |x + 3| by remοving the absοlute value bars:

|x + 3| = |(5 + positive real number) + 3|

= (8 + positive real number)|

= |8 < x < ∞|

Sο the simplified expressiοn fοr |x + 3|, when x > 5, is simply |8 < x < ∞|.

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Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

dy/dt = 0

-r/k y²+ry-h=0

y = k/2(1±√(1-4h/rk))

Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

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The probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

Given that the probability Kayla will score above 70% on a mathematics test is 0.60, and Kayla will take four tests this semester, and we want to find the probability she will score above 70% on exactly three out of the four tests, to determine what is the probability of Kayla scoring above 70% on exactly three out of the four tests, the following calculation must be performed:

Therefore, the probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.

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Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

Answer:

39886

Step-by-step explanation:

youre welcome :)

95% confidence interval for the ratio of medians is a range of values that we are confident contains the true population ratio, with a specified level of confidence.

A confidence interval is a range of values that we are confident contains the true population parameter, with a specified level of confidence. In this case, we are looking at the ratio of medians in the Verizon data and finding a 95% confidence interval for the ratio.

Let's say the sample median for the first data set is M1 and the sample median for the second data set is M2. The standard error for M1 and M2 can be calculated using the formula for the standard error of the median.

Next, we use the formula for a confidence interval for the ratio of medians:

=> (M1/M2) +/- (Z * SE(M1/M2)),

where Z is the critical value from a standard normal distribution for a 95% confidence level.

The percent bias is the difference between the estimated value and the true value, divided by the true value and expressed as a percentage. In this case, we will calculate the percent bias of the confidence interval for the ratio of medians relative to the standard error.

Finally, we compare the results for the ratio of medians with the results for the ratio of means. This comparison can give us an idea of the difference in the level of accuracy and precision between the two estimates.

Complete Question:

Consider the Verizon data. find a 95% confidence interval for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means

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Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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Answer:

1.375 decimal to fraction.

2/7 Fraction to Decimal

Step-by-step explanation:

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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Step-by-step explanation:

when 11 is decreased by a number, the result is 413

Answer:

the way in which factors are grouped in a multiplication problem does not change the product.

Step-by-step explanation:

Answer:

D. all real numbers

Step-by-step explanation:

i think this is the answer sorry if you get it wrong.

Answer:

(0, 4)

Step-by-step explanation:

The y-intercept is defined as the point where the line intersects the y-axis. All we need to do is find where the line intersects the y-axis.

(0, 4) is the answer.

Answer:

The independent variable is the time spent drive and the dependent variable with the amount of gas in the tank

Step-by-step explanation:

Does the gas in the tank depend on the time driving or does the time driving depend on the amount of gas in the car.

The amount of gas is the tank is determined by how much time the car is driven.

Based on the information given about the geometry, the value of CF will b A. 6cm.

Since OE and OF are both 4 cm, then OEF is an equilateral triangle. This means that EOF is 60 degrees.

Since AB is 12 cm, then AB is twice the length of OE. This means that ABE is a 30-60-90 triangle.

In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30 degree angle. This means that CF is 6 cm.

In conclusion, the correct option is A.

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Answer:

Find the value of sin 135.

We have to find the value of sin 135º

Solution

sin(135) can be expressed as = sin (90 + 45)

Using the identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B) we will expand the above sin value

= sin (90 + 45) = sin(90)cos(45) + cos(90)sin(45)

On substituting the known values we get

= ( 1 x 1/√2) + (0 x 1/√2)

= 1/√2

= 0.7071067. . .

Answer

Hence the value of sin 135º=  1/√2 or sin 135º= 0.7071067.

Step-by-step explanation:

this would be correct.

The required value of  sin 45° and sin 135º is \(\frac{\sqrt{2} }{2}\)  and \(\frac{1}{\sqrt{2} }\).

The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Given:

The given right triangle having it sides are 1 ,1, \(\sqrt{2}\).

According to given question we have

By the formula of trigonometry we get ,

This is a common value, in which

sin 45º=\(\frac{1}{\sqrt{2} }\)

We can now rationalize the fraction, which comes out to:

=

\(\frac{1}{\sqrt{2} } *\frac{1}{1} \\\\=\frac{1}{\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} }\\\\=\frac{\sqrt{2} }{2}\)

The common value of sin(135) can be expressed as

= sin (90 + 45)

By using the identity

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

= sin (90 + 45) = sin(90)cos(45) + cos(90)sin(45)

On substituting the known values we get,

\(= ( 1 * \frac{1}{\sqrt{2} } ) + (0 *\frac{1}{\sqrt{2} } )\\=1/\sqrt{2.\)

Therefore, the required value of  sin 45° and sin 135º is \(\frac{\sqrt{2} }{2}\)  and \(\frac{1}{\sqrt{2} }\).

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Answer:

Choice C

Step-by-step explanation:

If L represents the number of losses, and each loss decreases the total ticket price ($47.48) by $0.29, then the equation can be written as the following

47.48 - 0.29L
If you plug in any value, larger than 0, you will see that the price decreases by a constant rate of $0.29

Hope this helps!!

Answer:

47.48/0.29=163.7241379

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

he would go to the barber shop 21 times in 2 years

Step-by-step explanation:

divide 4 by 52 and then multiply by 2

Answer:

26

Step-by-step explanation:

52÷4 = 13 times a year

therefore, for two years

13 × 2 = 26

The scale factor of the given square pyramid is: 4:5

We are given the volume of the square pyramids as:

Volume of Small Pyramid = 64 in³

Volume of Large Pyramid = 125 in³

The volume of this square pyramid is usually:

Volume = side * side * side

V = s³

The size by which this square pyramid is enlarged or reduced is referred to as its scale factor. It is normally utilized when there is a need to increase the size of a 2D shape like circle, triangle, square, rectangle, etc. If y = bx is an equation, then it means that b is the scale factor for x.

Thus:

Scale factor will be the ratio of the sides of the pyramids.

Scale factor = (∛64)/(∛125)

Scale Factor = 4/5 = 4:5

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