factorize 4x²+17x-15​

The total cost for each combination with the special offer would be:

Massage, leg wax, and manicure: £68.25

Massage, facial, and eyelash tint: £59.25

Massage, leg wax, and eyelash tint: £57.75

We can try out the different possibilities and calculate the total cost of each.

Let's start by listing the prices of the treatments she's interested in:

Massage: £35

Facial: £31

Leg wax: £29

Manicure: £27

Eyelash tint: £13

Now, we can try out the different combinations of 3 treatments and calculate their total cost:

Massage, facial, and leg wax:

Total cost = £35 + £31 + £29 = £95

With 25% off, the cost would be £71.25, which is over Lou's budget of £60, so this combination is not possible.

Massage, facial, and manicure:

Total cost = £35 + £31 + £27 = £93

With 25% off, the cost would be £69.75, which is still over Lou's budget of £60, so this combination is also not possible.

Massage, leg wax, and manicure:

Total cost = £35 + £29 + £27 = £91

With 25% off, the cost would be £68.25, which is within Lou's budget of £60. Therefore, this combination is possible.

Massage, facial, and eyelash tint:

Total cost = £35 + £31 + £13 = £79

With 25% off, the cost would be £59.25, which is within Lou's budget of £60. Therefore, this combination is also possible.

Massage, leg wax, and eyelash tint:

Total cost = £35 + £29 + £13 = £77

With 25% off, the cost would be £57.75, which is within Lou's budget of £60. Therefore, this combination is also possible.

From the above calculations, we can see that Lou can choose from three possible combinations of treatments that fit within her budget and qualify for the special offer:

Massage, leg wax, and manicure

Massage, facial, and eyelash tint

Massage, leg wax, and eyelash tint

The total cost for each combination with the special offer would be:

Massage, leg wax, and manicure: £68.25

Massage, facial, and eyelash tint: £59.25

Massage, leg wax, and eyelash tint: £57.75

Therefore, Lou can choose any of the above combinations and pay the corresponding total cost to enjoy the special offer.

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The cmy values for red are (0%, 100%, 100%). This means that there is no cyan present, but there is 100% magenta and 100% yellow present to create the color red.

Cyan, Magenta, and Yellow, the three primary colours used in subtractive colour mixing, are abbreviated as cmy values. A value between 0 and 100 is used to represent each colour and denote the proportion of that colour in a given colour mixing.

It is important to note that values like these are used in color printing to determine the amounts of cyan, magenta, and yellow inks needed to create a certain color. These values reflect the values of a subtractive color model, where colors are created by subtracting light from white.

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Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.

Answer:

-14

Step-by-step explanation:

Given -x+5y=7

Now we substitute x+5y into -2(-x+5y)

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

= - 14

The volume of the prism which is filled with 135 cubes is 5 cubic feet.

What is the Volume of Cube ?

The volume of a cube defines the number of cubic units, occupied by the cube completely. The unit of volume of the cube is in cubic units such as cu. centimeters, cu. meters, cu. inches, cu. feet, etc.

Here Prism is filled with 135 cubes.

Volume of prism = volume of 135 cubes

                            = 135 X side X side X side

                            = 135 X 1/3 X 1/3 X 1/3

                            = 135 / 27

Volume of prism = 5 cu. feet

Thus, The volume of the prism which is filled with 135 cubes is 5 cubic feet.

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If we want the margin of error for the 90% confidence level to be about 1.5%, then a sample of 3002 is recommended.

In this problem, we want to find n for which  the margin of error for the 90% confidence level to be about 1.5%

From part (a), the 90% confidence interval is (0.435, 0.525)

the margin of error M = 0.015

0.015 = 1.645√(0.48 * 0.52)/n

(√n) ² = (0.015)²

n = 3001.9

n ≈ 3002

Therefore, a sample of 3002 is recommended.

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The complete question is:

Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot a ord it. (a) Calculate a 90% con dence interval for the proportion of Americans who decide to not go to college because they cannot a ord it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% con dence level to be about 1.5%. How large of a survey would you recommend?

Algebraic expressions are mathematical statements made up of variables, constants, and operations, which can be simplified to -17x²+4x+5.

Given expression: -10x²+4x-7x²+5.A mathematical statement made up of variables, constants, and mathematical operations is known as an algebraic expression. It stands for a mixture of numbers and letters, where the letters are called variables and they can have various values. In algebra, relationships are represented and calculations are done using algebraic expressions.

The given expression can be simplified as:

Adding the like terms together,

we get,-10x²-7x²+4x+5

= -17x²+4x+5

Thus, the simplified expression is -17x²+4x+5.

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Answer:

60

Step-by-step explanation:

Answer:

should be 8

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

rise = 2 ft

run = 10 ft

slope = rise/run = 2/10 = 1/5

Answer: 1/5

Answer:

1/5

Step-by-step explanation:

The slope is the rise over the run

Y / x

2/10

1/5

Answer:

x = 20

Step-by-step explanation:

180° = total

3 = amount of angles

180 ÷ 3 = 60°

60° + 60° + 3x = 180°

120° + 3x = 180

3x = 180 - 120

3x = 60

x = 20

The number of 6-card hands  in which at least one card from each suit is equal to 8,184,220.

Total number of 6-card hands that can be formed from a deck of 60 cards is,

Using combination formula,

C(60, 6) = 50,063,860

Now, subtract the number of 6-card hands that do not contain at least one card from each suit.

There are 5 ways to choose the suit that will be missing from the hand.

Once this suit is chosen, there are 48 cards remaining in the other suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suit is,

C(48, 6) = 12,271,512

Overcounted the number of hands that are missing more than one suit.

There are C(5, 2) ways to choose 2 suits that will be missing from the hand.

Once these suits are chosen, there are 36 cards remaining in the other 3 suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suits is,

C(36, 6) = 1,947,792

We cannot have a 6-card hand that is missing more than 2 suits.

3 suits with no cards in the hand, which is not allowed.

Number of 6-card hands that have at least one card from each suit is,

C(60, 6) - 5×C(48, 6) + C(5, 2)×C(36, 6)

=50,063,860 - 5×  12,271,512 + 10 × 1,947,792

= 50,063,860 -61,357,560 + 19,477,920

= 8,184,220

Therefore, there are 8,184,220 of 6-card hands that have at least one card from each suit.

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Using Pythagoras theorem, we can find the value of as follows:

a = √48.

b = √96.

h = √32.

The three sides of a right-angled triangle are related, according to the Pythagorean theorem, which is often referred to as the Pythagorean relation.

According to the Pythagorean theorem, a triangle's hypotenuse square is equal to the sum of its other two sides squares.

Here in the right-angled triangle,

The equations that we can derive are as follows:

a² + b² = 12²

a² = 4² + h²

b² = 8² + h²

Now we have 3 equations.

Using the 2nd & 3rd equations in the 1st we get,

4² + h² + 8² + h² = 12²

⇒ 2h² + 16 + 64 = 144

⇒ 2h² = 144 - 80

⇒ h² = 32

⇒ h = √32.

Now putting the value of h in equation 2 and 3 we can get the values of a and b as follows:

a² = 4² + h²

⇒ a² = 16 + 32

⇒ a² = 48

⇒ a =√48.

b² = 8² + h²

⇒ b² = 64 + 32

⇒ b = √96.

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Answer:

95

Step-by-step explanation:

We know the measure of angle 4 is 85, therefore the measure of angle 2 is also 85.

Measure 2 is equal to measure 6, therefore measure 6 also equals 85, measure 8 equals measure 6 giving it the measure of 85.

Now the sum of angles 5 and 7 must equal 190, given we have two 85 degree angles, and the other two are equal, they must sum to 190, since they are equal we will divide 190 into 2, making angles 5 and 7 have a measure of 95.

Answer: 95°

Step-by-step explanation: With 2 parallel lines cut by a transversal, the following conditions are true.

Alternate interior angles are congruent. <4 and <6 are alternate interior angles, and so are <3 and <5.

Corresponding angles are congruent. Corresponding angles are angles that are in the same position in one line as the other. <1 and <5 are corresponding angles, and <4 and <6 are congruent. <2 and <6 are congruent, and <3 and <7 are congruent.

Vertical angles are congruent. Angles that are directly diagonal on the same line are congruent. <5 and <7, and <6 and <8 are examples of this.

Supplementary angles are, well, supplementary. By definition, two angles that are supplementary add up to 180°. Supplementary angles are angles that are on the same line and transversal, but not vertical angles. Rather, the angles are right next to teach other.

Alternate exterior angles are congruent. Alternate exterior angles are angles that are like alternate interior angles, but both share a position on the outside (and are diagonal.) The alternate exterior angles are <2 and <8, and <1 and <7.

Now that we have all definitions and conditions at hand, this will be easy.

If m<4 is 85°, and we want m<5, then we can see that <4 and <3 are supplementary angles. So by definition, <4 + <3 = 180°. We can substitute in <4 since we know it. We get 85° + <3 = 180°. Subtracting 85° from both sides, we get <3 = 95°.

Now we see <3 and <5 are alternate interior angles. By definition they are congruent. Thus, m<5 is 95° too.

Hope this helped!

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The correct function that matches the data in the graph is  a(n) = 46-(n-1)-4 (option C)

The only way is to verify the function matches the data by replacing n.

For example, we know at 5 seconds the temperature is 30. Let's use 5 (n) to verify the function.

This option matches the value of the temperature.

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Yes, q = -5 is a solution to the inequality q < -7.

We have,

To determine if q = -5 is a solution to the inequality q < -7, we need to plug in -5 for q in the inequality and see if it is a true statement.

Substituting q = -5.

-5 < -7

Since -5 is less than -7,

The inequality q < -7 is true when q = -5.

Thus,

q = -5 is a solution to the inequality q < -7.

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The area under the standard normal curve where P(-1.19 < Z < 0) is approximately 0.3830, which corresponds to answer choice (c).

The area under the standard normal curve where P(-1.19 < Z < 0), can be found by following steps,

1. Look up the z-scores in the standard normal distribution table (also known as the Z-table).
2. Subtract the area corresponding to the lower z-score from the area corresponding to the upper z-score.

For Z = -1.19, the area to the left is approximately 0.1170. For Z = 0, the area to the left is 0.5 (since the normal curve is symmetrical, and Z = 0 is at the center).

Subtract the area corresponding to the lower z-score from the area corresponding to the upper z-score: 0.5 - 0.1170 = 0.3830.

Therefore, the answer choice (c) corresponds to the region under the standard normal curve where P(-1.19 Z 0) is roughly 0.3830.

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The value of latoken in 2027 is $4731.

Given that in 2025 digital wallet users at $19900 and in 2027 latoken international clients will be $1000 and the number of monthly paying clients will grow from 30,000 at a 10% monthly rate till 2027 and 0 afterward.

The time esteem of cash states that a sum of cash is esteemed more presently than it'll be within the future. This is often due to the fact that cash can as it was extended by means of speculation. Speculation that's put off could be a missed opportunity. The time esteem of cash equation takes into consideration the amount of cash, its future esteem, the sum it can create, and the time period. The number of compounding periods is additionally a key variable for investment funds accounts.

By 2025=19900

By 2027 =1000 for client

Monthly pay =30000 each month

Rate=10%

At the end  the value is computed below:

AED=30000(1+0.1)¹²

AED=30000(1.1)¹²

AED=30000×3.138

AED=94140

To find the value computation is done below:

19900x=1000×v×AED

x=(94140×1000×140)/19900

x=4.731×1000

x=4731

Hence, the value of latoken in 2027 when digital wallet user at $19,900 by 2025 and latoken international client will be $1000 in 2027 is $4731.

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Answer:

d for sure

Step-by-step explanation:

Answer:

B. (2, 1)

Step-by-step explanation:

The coordinate of C is the point at which point A and B meet after being extended

Answer: 94.8

Step-by-step explanation:

To find this, you need half of 63.2 which is 31.6. Then add that to 63.2 and bam, your answer.

Answer:

94.8g of sugar

Step-by-step explanation:

Set up a ratio- \(\frac{63.2}{8} =\frac{?}{12}\)

cross multiple- \(12*63.2=8*?\)

solve- \(758.4 = 8*?\)

divide by 8- \(758.4/8 = 94.8\)

The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

Explain the divisibility test of 11.

For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.

Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11

Required 5 digit number is of the form, ab,cba

Using the divisibility test of 11, we get

(b + b) - (a + c + a) to be divisible by 11

i.e. 2b - (2a + c) to be divisible by 11

Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11

78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Thus, a positive 5-digit number is 87,978

Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

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To prove that if a 3x3 matrix A with real entries is not similar over R (the field of real numbers) to a triangular matrix, then A is similar over C (the field of complex numbers) to a diagonal matrix, we can use the theory of eigenvalues and eigenvectors.

First, let's assume that A is not similar over R to a triangular matrix. This means that A does not have three linearly independent eigenvectors over R.

By the fundamental theorem of algebra, we know that every polynomial of degree n has n complex roots, counting multiplicities. Since A is a 3x3 matrix, its characteristic polynomial has degree 3, which means it has 3 complex roots.

Since A does not have three linearly independent eigenvectors over R, there must be at least one complex eigenvalue, which corresponds to a complex root of the characteristic polynomial. Let λ be a complex eigenvalue of A.

Since A has real entries, its complex eigenvalues must occur in conjugate pairs. Let μ be the complex conjugate of λ.

Now, consider the matrix B = P^(-1)AP, where P is the matrix whose columns are the eigenvectors corresponding to the eigenvalues λ and μ.

By construction, B is a complex matrix, and it is easy to see that B is diagonal, with diagonal entries being the eigenvalues λ and μ.

Therefore, A is similar over C to a diagonal matrix.

In conclusion, if A is not similar over R to a triangular matrix, then A is similar over C to a diagonal matrix.

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To maintain a familywise significance level of 0.1 across all ten hypothesis tests use a significance level of 0.01.

To maintain a familywise significance level of 0.1 for ten hypothesis tests, you need to adjust the significance level for each individual test to account for multiple testing.

One commonly used method is the Bonferroni correction.

The Bonferroni correction involves dividing the desired overall significance level (0.1) by the number of tests (10) to obtain the adjusted significance level for each individual test.

Adjusted significance level = Overall significance level / Number of tests

Adjusted significance level = 0.1 / 10 = 0.01

Therefore, for each individual test, you should use a significance level of 0.01 to maintain a familywise significance level of 0.1 across all ten hypothesis tests.

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