Evaluate the logarithm

The graphs of these two equations intersect in 4 points.

What is an example of a hyperbola?

A hyperbola is a collection of points in a plane whose separations from two fixed points, known as its foci (plural of focus), differ by an amount that is always the same.

                    Using the figure as an example, a hyperbola with foci at (-3,0) and The point at illustrates its constant distance as being 4. (-3,-2.5).

x²+y²=25

it is a circle with radius=5

x²-y²=3

it is a hyperbola.

x²-y²=3

so, they intersect in four points.

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The complete question is -

The graphs of these two equations intersect in how many points?

x^2+y^2=25

x^2-y^2=3

Price of a gallon of gasoline at the beginning of July was $2.41

What is percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

According to the question:

In July, the price of a gallon of gasoline rose=12%

In august, it fell 15% of its final July price,

Ending the month at 1.19 rupees

Let us consider,

x is the original price at the beginning of July,

then the price of gasoline rose is 112%

=100+2

=112%

=112/100

=1.12

In august it fells 15%=100-15%

=.85%

With the help of given data

the original price is---- x

(1.12) × (.85) x = 2.29

find the value of x

x = 2.29/0.952

x=2.41

x=2.41 was its price at the beginning of July.

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At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.= ​∗e −1.5 ≈0.777.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

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

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

I If X indicates the number of patients who arrived in 1.5 hours at random, then X = Pois(6*1.5) = Pois (9)

P(X=7)=frac 9/7/7!e-9/approximately 0.17P(X=7)= 7! 9/7

​ \s ∗e \s−9 \s ≈0.117

(ii) If X indicates the number of patients who arrived in 15 minutes or less, then X = Pois(6*0.25) = Pois (1.5)

At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.

P(X≥1)=1-P(X<1)

=1-P(X=0)

=1-frac 1.5 0 0!*e 1.5 Approximately 0.777P(X1)

=1−P(X<1)

=1−P(X=0)=1− \s0! \s1.5 \s0

​ \s ∗e \s−1.5 \s ≈0.777

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The indicated critical value of Z for given significance level, α = 0.04 is 1.75..

The critical Z-value is the point at which the area below the standard normal distribution is cut off. A critical value of z can indicate the probability that a particular variable has. If the absolute value of the test statistic is greater than the critical value, statistical significance is declared and the null hypothesis is rejected. The critical values of Z and t are approximately the same. The critical value test is:

Steps to determine the critical value:

We have given that,

α = 0.04 then α/2 = 0.02

then 1 - 0.02 = 0.98

Using the Z-table,

p-value = 1.7911 4444 ~ 1.75

Hence the critical values z, 0.04, is 1.75

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After 1 week Luca and his friend  will have passed the same number of scales and the number of scales = 11

In this question, we have been given a situation.

we need to write a system of equations to describe the situation.

Let x be the number of weeks and y be the number scales.

luca has passed 9 scales, whereas his friend warren has passed 8 of them. going forward, luca has committed to passing 2 scales per week, and warren has committed to passing 3 per week.

So, we get a system of equations as:

y = 2x + 9

y =  3x + 8

We need to find the amount of time(weeks) it would take that the two friends will have passed the same number of scales.

Also, we need to find the number of scales.

When the two friends will have passed the same number of scales,

2x + 9 =  3x + 8

3x - 2x = 9 - 8

x = 1

After 1 week the two friends will have passed the same number of scales.

And  the number of scales would be,

y = 11

Therefore, after 1 week the two friends will have passed the same number of scales.

And  the number of scales would be 11

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The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

Given that,

a to b is translated by the vector (4/-3)

We have to find what is the vector converting b to a.

We know that,

Quantities with both magnitude and direction are referred to as vectors. Additionally, it refers to the type of the quantity.

Here,

We have a vector,

ab=(4/-3)

Its direction will be reversed to translate the vector in the other way,

For

ba=-(4/-3)

ba=4/3

Therefore, The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

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The probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

Given that,

Poisson (2.)

Let x = The number of pairs of twins

That will be born in the Country in 2015

To find : Calculate the probability that exactly 18 pairs of twins will be born in the country in 2015.

We know that

Here,

The probability mass function (pmt of x) is given by

P ( X = x ) = e⁻²¹ x 21ˣ / x!

where x = 0,1,2 , . . .

Substitute x = 18 in above equation,

Then we get,

P ( x = 18 ) =  e⁻²¹ x 21¹⁸ / 18!

P( x = 18 ) = 0.07472

P ( x = 18 ) = 0.07472

Therefore, the probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

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Answer: x can equal 9 or -1

Step-by-step explanation:

Answer:

Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Step-by-step explanation:

To determine at which point Plan A is a better deal than Plan B, we need to compare the total cost of each plan for a given amount of data usage.

The total cost of Plan A for 3GB of data is $52 per month. For every additional GB of data, the cost is $3, so if we use x GB of data beyond the included 3GB, the total cost of Plan A would be $52 + $3x.

The total cost of Plan B for 5GB of data is $65 per month. For every additional GB of data, the cost is $1.75, so if we use x GB of data beyond the included 5GB, the total cost of Plan B would be $65 + $1.75x.

To determine at which point the total cost of Plan A is less than the total cost of Plan B, we can set the two equations equal to each other and solve for x:

$52 + $3x = $65 + $1.75x

$1.25x = $13

x = $13 / $1.25

x = 10.4

Therefore, Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Answer:

A

Step-by-step explanation:

The value of the test statistic = 2.06

What is Statistic ?

The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.

What is normally distribution?

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

Given,

weights of sugar bags are normally distributed.

Sample mean=5.2

sample standard deviation = 0.2366

Test statistic

t = x(bar) -µ/σ [tex]\sqrt{n}[/tex]

= 5.2-5/0.2366/[tex]\sqrt{6}[/tex]

= 2.0705

The test statistic's value is 2.06

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The equation (C) (x + 2) (x - 1) = x² - 2x - 3 is not a quadratic equation.

A quadratic equation is any algebraic expression that can be expressed in proper format where x represents an unknown value, a, b, and c represent known values, and where a 0 is true.

(A) (x + 2)² = 2(x + 3)

Algebraic identity is used:

(a + b)² = a² + 2ab + b²

x² + 4x + 4 = 2x + 6

x² + 4x - 2x + 4 - 6 = 0

x² + 2x - 2 = 0

The equation has a degree of two.

As a result, the equation (x + 2)² = 2(x + 3) is quadratic.

(B)  x² + 3x = (-1) (1 - 3x)²

Algebraic identity is used:

(a - b)² = a² - 2ab + b²

x² + 3x = -1(1 - 6x + 9x²)

x² + 3x = -1 + 6x - 9x²

x² + 9x² + 3x - 6x + 1 = 0

10x² - 3x + 1 = 0

The equation has a degree of two.

As a result, the equation (x + 2)² = 2(x + 3) is quadratic.

(C) (x + 2) (x - 1) = x² - 2x - 3

According to the multiplicative and distributive properties:

x² - x + 2x - 2 = x² - 2x - 3

x² - x² - x + 2x + 2x - 2 + 3 = 0

3x + 1 = 0

The equation has a degree of 1.

As a result, the equation (x + 2) (x - 1) = x² - 2x - 3 is not quadratic.

Therefore, the equation (C) (x + 2) (x - 1) = x² - 2x - 3 is not a quadratic equation.

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Answer: p = 3

Step-by-step explanation:

7−4p−(−5)

7-4p + 5

Because negative one times negative five equal positive 5

12 - 4p

To solve further

-4p = -12

p = 3

The answer is true.

When a child presents with commonly occurring phonological patterns such as fronting, cluster reduction, stopping, and final consonant deletion, the minimal pairs approach readily comes to mind as an option. Not only are there a lot of meaningful minimal pair contrasts that you can use as part of therapy, but these developmental patterns were the ones that the majority of researchers targeted in their studies. We’ve established what developmental phonological error patterns are, but some children present with unusual or non-developmental patterns. Studies have used this approach with patterns such as backing and medial consonant deletion. Dodd et al., (2003) actually recommend prioritising those non-developmental error patterns over developmental ones.

It's true due to one of the reasons why it is important to learn the minimal pair's approach is that it can be used with a large range of severity, from mild-severe phonological impairments. If the child has a severe-profound phonological impairment, Williams (2000a) suggests that students are best suited to another approach.

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Step-by-step explanation:

8.

the angle at a vertex (crossing point) outside of the circle (when both lines intersect with the circle arc, which is also the case for tangents) is half of the difference of both arc angles (the outer and the inner angles).

the outer angle is 250°. since the full circle is 360°, this makes the inner arc angle 360-250 = 110°.

the difference is 250-110 = 140.

and half of that difference is

140/2 = 70°.

so, x = 70°

9.

see 8.

the angle at the vertex outside the circle is half of the difference between outer and inner arc angle.

in fact, this is again about tangents (despite the picture), because the outer angle + the inner angle is again 360° (the full circle). this can only be, if the 2 lines are tangents splitting the outer and inner arc angles into 2 parts of 360° without remainder.

320 - 40 = 280

280/2 = 140

x = 140°

10.

see 8. and 9.

it is an extreme example, where the vertex of the 2 intersecting lines is exactly on the circle arc and the tangent point of the second line.

this makes the inner arc angle = 0°.

remember, the vertex angle (55°) is half of the difference of the outer (x) and inner (0°) arc angle.

55 = (x - 0)/2

110° = x

11.

remember the table question, where we found that the circle internal angle of 2 intersecting lines is half of the sum of both intersected arc angles ?

this is exactly this case again.

(120 + 50)/2 = 170/2 = 85°

x = 85°.

12.

first, like in 8. and 9., we determine the vertex angle. x is then the supplementary angle (together they have 180°) to this vertex angle, because the sum of all angles around one point on one side of a line is always 180°.

the vertex angle is

(125 - 15)/2 = 55°

x + 55 = 180

x = 125°.

13.

see 11.

the circle internal vertex angle is half of the sum of both circle arcs.

x = (70 + 30)/2 = 100/2 = 50°.

14.

again, an extreme case, where the vertex is on the circle arc. so, the second arc angle is 0°.

see also 12.

x is the supplementary angle of the vertex angle.

the vertex angle is

(80 + 0)/2 = 80/2 = 40°.

x + 40 = 180

x = 140°.

15.

it is difficult to read. I see the outer arc circle as 140°.

see 8., 9., 10.

the vertex angle x is

x = (140 - 70)/2 = 70/2 = 35°

do I sound like a broken record ? I at least feel that way. you should be able to apply the explanations from the previous questions to solve the new ones yourself.

what is not clear yet ? where do you need further explanations ?

The equation that can be used to find {p}, the number of pieces Joy and her brother ate is : {p} + 4 = 16.

Given is that Joy baked 2 pizzas and cut each pizza into 8 pieces. Joy and her brother ate all but 4 pieces of pizza.

We can write the equation {p} as -

2 x 8 = 4 + {p}

{p} + 4 = 16

Therefore, the equation that can be used to find {p}, the number of pieces Joy and her brother ate is : {p} + 4 = 16.

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{Question in english language is -

Joy baked 2 pizzas and cut each pizza into 8 pieces. Joy and her brother ate all but 4 pieces of pizza. What equation can be used to find p, the number of pieces Joy and her brother ate?

The simplification of [tex](16)^{1/2}[/tex] is 4.

To simplify [tex](16)^{1/2}[/tex] , you can use the property of exponents that says that [tex]{(a^b)}^c = a^{(b*c)[/tex]. Therefore, [tex](16)^{1/2}[/tex] can be rewritten as [tex]16^{(1/2)}[/tex].

The square root of 16 is 4, so [tex]16^{(1/2)}[/tex] = 4. Therefore, [tex](16)^{1/2}[/tex] = 4.

You can also simplify [tex](16)^{1/2}[/tex]  by writing 16 as a product of its prime factors: 16 = [tex]2^4[/tex]. The square root of 16 is the same as the square root of 2^4[tex]2^4[/tex], which is [tex]2^{(4/2) = 2^2} = 4[/tex]. Therefore, [tex](16)^{1/2}[/tex] = 4.

Simplification is a process of making something simpler or easier to understand. This can be done by reducing the complexity of a system, removing unnecessary components, or making the language more concise.

Simplification complexity is the process of reducing the complexity of a problem, system, or process. This can involve breaking down a complex problem into smaller, more manageable parts, or reorganizing the system or process to make it simpler and easier to understand and use. Simplifying complexity can make a system or process more efficient and easier to maintain.

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The computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10.

This statement is a false statement.

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample. First, a hazy assumption about the parameter or distribution is made.

The null hypothesis is that 50% is true, while the alternative hypothesis is that 50% is not accurate, for instance, if someone wants to test whether a penny has an exact 50% chance of landing on heads.

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Answer:

1/4 as a percent is 25%

25% as a decimal is .25

Step-by-step explanation:

1/4 is one quarter, .25

25%, move the decimal to the left twice

25----> 2.5------> .25

Answer:  The graph is shown below. It is nonlinear

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

Explanation:

I used GeoGebra to make the graph. Desmos is another option I recommend.

The equation we graph is y = (1/2)^x since we're splitting the paper in half each time. This is an exponential decay function. Note how the curve slopes downhill when moving to the right.

It appears the curve touches or crosses the x axis; which is misleading. Instead, the curve is getting closer and closer to this horizontal asymptote. It will never reach the x axis. Think of it like an electric fence.

As the graph indicates, we don't have a straight line. Therefore, the function isn't linear. It's a nonlinear curve.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

A box of cookies contains 12 chocolate-chip cookies, 6 peanut-butter cookies, and 6 sugar cookies.

Total number of cookies = 12 + 6 + 6 = 12 + 12 = 24

Now,

The probability of randomly selecting a chocolate-chip cookie.

= 12/24

= 1/2

The remaining chocolate.

= 24 - 1

= 23

Now,

The probability of randomly selecting a sugar cookie.

= 6/23

Now,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie

= 1/2 X 6/23

= 3/23

Thus,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

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Alexa's non-taxable income will be equal to $603.3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Alyssa started working making $14.75 per hour. She worked a total of 48 hours during the last pay cycle. Her taxes totalled $104.22.

The non-taxable income will be calculated as,

Total income = 14.75 x 48 = 707.52

Non-taxable income = 707.52 - 104.22

Non-taxable income = $603.3

Therefore, Alexa's non-taxable income will be equal to $603.3.

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Answer:

x= -2

y= 0

Step-by-step explanation:

isolate y in second equation

-3x=6-y

 +y.   +y

-3x+y=6

+3x.    +3x

y=3x+6

now we know y is the same as 3x+6 we can put it into the first equation where y is

-4x+2(3x+6)=8

-4x+6x+12=8

2x+12=8

   -12.  -12

2x= -4

/2.  /2

x= -2

now fill in x to find y

-3(-2)=6-y

6=6-y

-6. -6

0= -y

/-1. /-1

0 =y

hopes this helps please mark brainliest

The missing statements and reasons in the proof are:

R3: Alternate Interior ∠s theorem

S4: Reflexive property

R5: ASA

A proof involves statements that are stated on one column, then followed by reasons that justify the statements stated, on another column.

The missing statements and reasons in the given proof above are explained below:

Statement                                                    Reason                                            

1. Parallelogram ABCD with diagonal AC  1. Given

2. AB║CD and AD║BC                               2. Def. of parallelogram

3. ∠1 ≅ ∠2 and ∠3 ≅ ∠4                             3. Alternate Interior ∠s theorem

4. AC ≅ AC                                                  4. Reflexive property

5. ΔABC ≅ ΔCDA                                       5. ASA

6. AB ≅ CD and AD ≅ BC                          6. CPCTC

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Answer:

Angle = 71.08°

Step-by-step explanation:

Since we're given all of the sides, we're able to use any one of the trigonometric proportions.  I can go through all three to show how they all yield the same answer.

The sine proportion is [tex]\frac{opposite}{hypotenuse}[/tex]

Using the ? angle as our reference angle (which we can refer to as "a" for the sake of the math), the side measuring 70 units is the opposite side and the side measuring 74 units is the hypotenuse:

[tex]sin (a)=\frac{70}{74}\\ sin^{-1}=\frac{70}{74}=a = 71.07535558=71.08[/tex]

The cosine proportion is [tex]\frac{adjacent}{hypotenuse}[/tex]

Using a as our reference angle still, the side measuring 24 units is the adjacent side and the side measuring 74 units is the hypotenuse:

[tex]cos (a)=\frac{24}{74}\\ cos^-^1=\frac{24}{74}=71.07535558=71.08[/tex]

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex]

Using a as our reference angle still, the side measuring 70 units is the opposite side and the side measuring 24 units is the adjacent side:

[tex]tan(a)=\frac{70}{24}\\ tan^-^1=\frac{70}{24}=a=71.07535558=71.08[/tex]

Again, just use the steps for either one of the three trigonometric proportions

Answer:

y = - 8x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 8 and c = 5 , then

y = - 8x + 5 ← equation of line

Using Percentage concept, Kareem had $7939 at the end of last year

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

In this problem, we could attempt to use reverse of simple interest formula, however, we can directly find 6.6% of 8500 and subtract it from the principal.

This is calculated as;

6.6/100 = x / 8500

0.066 = x / 8500

x = 8500 * 0.06

x = 561

The investment decreased by $561

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The simplest form in fraction will be 20666667/1000000 that can be find out using decimal and fraction relation.

How to convert decimal to fraction?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value.

For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.

Steps :
1. Write down the decimal divided by 1, like this: decimal/1

2. Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

3. Reduce the fraction.

In given que 2.0666667 ,

7 decimal points are here.

so, equation will be 20666667/10^7

i.e. 20666667/10000000.

As both no. is indivisible to each other

So this is the simplest from.

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Answer: y = 3x - 8

Step-by-step explanation:

      We will write a point-slope equation to help us write a slope-intercept equation.

y - 16 = 3(x - 8)

y = 3(x - 8) + 16

y = 3x - 8

      The slope-intercept form equation that represents this line is;

                        y = 3x - 8

The total time ran by Katie on Tuesday and Wednesday together is given by the equation A = 16.23 minutes

where A is the total time

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time ran by Katie on Tuesday and Wednesday be = A

Now , the equation will be

The time required by Katie to run a mile on Tuesday = 8.34 minutes

The time required by Katie to run a mile on Wednesday = 7.89 minutes

So ,

Total time ran by Katie on Tuesday and Wednesday A = time required by Katie to run a mile on Tuesday + time required by Katie to run a mile on Wednesday

Substituting the values in the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 8.34 minutes + 7.89 minutes

On simplifying the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 16.23 minutes

Therefore , the value of A is 16.23 minutes

Hence , The total time ran by Katie on Tuesday and Wednesday together is A = 16.23 minutes

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