In a party of 60 people, 35 had vanilla ice-cream, 35 had chocolate ice-cream. All the people has at least one ice cream then how many of them had i) both vanilla and chocolate ice-cream ii) only Vanilla ice-cream iii) Only chocolate ice-cream​

Answer:5/2a + 10/3b

Step-by-step explanation:

(1/6)(15a+20b)

=(1/6)(15a)+(1/6)(20b)

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

Step-by-step explanation:

a.) 13/3  *6

= 78/3

=26

b.) 13/5 * 10/3

= 130 / 15

= 26/3

Answer: C; 5.32

Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!

Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer: 4/33

Step-by-step explanation:

just divide

Answer:

The answer is 4/33.

Step-by-step explanation:

to get this you just have to divide.

you're welcome.

The income tax with the IRA is $6,582 and the income tax without the IRA is $5,774.

Without the IRA, his taxable income would be his gross income minus the standard deduction for a single taxpayer with no dependents, which is $12,550 in 2023:

Taxable income without IRA = $49,000 - $12,550 = $36,450

Using the tax table for single taxpayers, we can find that his income tax would be $5,773.75.

With the IRA, his taxable income would be his gross income minus the amount deposited into the IRA over the course of the year. Since he is depositing $589 each month, the total deposited in a year would be $589 * 12 = $7,068.

Taxable income with IRA = $49,000 - $7,068 = $41,932

Using the same tax table, we can find that his income tax with the IRA would be $6,581.63.

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Answer:

$180

Step-by-step explanation:

10+30+30+100+10=180

Answer:

3 more picks

Step-by-step explanation:

710 divided by 5 = 142

The requried, probability that both the first digit in the last digit of the three-digit number is even numbers is 20%.

To count the number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9, we can use the permutation formula:

P(n, r) = n! / (n-r)!

In this case, we have n = 6 (since we have 6 digits to choose from) and r = 3 (since we want to form three-digit numbers). Using the formula, we get:

P(6, 3) = 120

We can choose the first digit in two ways (2 or 8), and we can choose the last digit in three ways (2, 8, or 6). For the middle digit, we have four digits left to choose from (1, 3, 5, or 9), since we cannot repeat digits. Therefore, the number of three-digit numbers with distinct digits that have an even first and last digit is:

2 x 4 x 3 = 24

The total number of three-digit numbers with distinct digits is 120, so the probability that a randomly chosen three-digit number with distinct digits has an even first and last digit is:

24/120 = 0.2 or 20%

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The side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.

Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.

Let's analyze the angles:

Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.

Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.

Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.

Based on these observations, we can order the side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

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Answer:

$374,080.00

Step-by-step explanation:

You want to calculate the interest on $40000 at 5.8% interest per month after 12 year(s).

The formula we'll use for this is the simple interest formula, or:

\(I=P*R*T\)

Where:

P is the principal amount, $40000.00.

r is the interest rate, 5.8% per month, or in decimal form, 5.8/100=0.058.

t is the time involved, 12....year(s) time periods.

Since your interest rate is "per month" and you gave your time interval in "year(s)" we need to convert your time interval into "month" as well.

Do this by multiplying your time, 12 year(s), by 12, since there's 12 months in 1 year.

So, t is 144....month time periods.

To find the simple interest, we multiply 40000 × 0.058 × 144 to get that:

The interest is: $334080.00

Usually now, the interest is added onto the principal to figure some new amount after 12 year(s),

or 40000.00 + 334080.00 = 374080.00. For example:

If you borrowed the $40000.00, you would now owe $374080.00

If you loaned someone $40000.00, you would now be due $374080.00

If owned something, like a $40000.00 bond, it would be worth $374080.00 now.

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

Answer:

m<MLO = 120°

Step-by-step explanation:

Equilateral Triangles have all 60° angles.

m<MLN = m<OLN = 60°

60°+60°=120°

The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2\)

So, we have:

\(d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2\)

d1 = 12

\(d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2\)

d2 =5

\(d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2\)

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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Answer:

ang hirap naman plss answee

Answer:

B) 10 units

Step-by-step explanation:

Area of a square is A = s², and perimeter of a square is P = 4s.

A = P + 60

s² = 4s + 60

s² − 4s − 60 = 0

(s + 6) (s − 10) = 0

s = -6 or 10

Since s can't be negative, s = 10 units.

I can not see the photo

9514 1404 393

Answer:

  A.  x -4y

Step-by-step explanation:

The first expression factors as ...

  = 2x(x -4y)

The second expression factors as ...

  = 3x^2(x -4y)

Factors that are common between these factorizations are ...

  x, (x -4y)

Of these, the one on your list of choices is ...

  x -4y

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

I'm not really sure what you mean by the numbers because that's alot.

Step-by-step explanation:

But all you have to do is:

Plus the morning and evening amount and then times it by 5

Like this: y + z x 5

I hope this helped!
Sorry if it didnt...

But have a nice day

Answer:

3.16227766017 is the answer

Answer: 3.16227766017

Step-by-step explanation:

Or you could round and get 3.2 or 3.16

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Translate

"Five" = 5

"times" is multiplication

"difference" is subtraction

"twice" means 2 times something

"a number" = x

"is" means equal

"-10" = -10

Step 2: Set up equation

5(2x - 4) = -10

Step 3: Solve for x

Authors provide solid justifications, The owners insisted that during the work hours the grinding never stop, no matter what."

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Answer:

1. 10/7, 2/1, 1,5

2. 5/8 * 3/2

Step-by-step explanation:

(:

Answer:

Which part exactly.. Or which number exactly

Answer:

57327392393629324

Step-by-step explanation:

The volume of the shape to the nearest tenth is equal to 138.4π m³.

In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

Volume of a sphere = 4/3 × π × 4.7³

Volume of a sphere = 138.4π m³

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Probability of defect per blade = 1/500 = 0.002

Poisson distribution :

Pₓ (k) = (x ^k)/k × e⁻ˣ

Where k = The number of defective blades in a packet.

For a packet of 10 blades the mean number of defect x = 0.002 × 10 = 0.02

1.) When k = 0

Pₓ(0) = (0.02⁰ / 0!) × e - 0.02 = 0.980199

The approximate number of packets containing blades with no defective is :

10000 × 0.980199 = 9802

2.) When k = 1

Pₓ(1) = (0.02 / 1!) × e-0.02 = 0.019604

Approximate number containing one defective is :

10000 × 0.019604 = 196

3.) When k = 2

Pₓ(2) = (0.02² / 2!) × e - 0.02 = 0.000196

Approximate number containing 2 defective :

0.000196 × 10000 = 1.9 = 2

4.) When k = 3

Pₓ(3) = (0.02³ / 3!) × e-0.02 = 0.000013

Approximate number containing 3 defective is :

0.000013 × 10000 = 0.13 = 0

Answer:

no defective blades in a consignment of 1,00,000 packets is 99837.

Step-by-step explanation:

we first need to find the mean number of packets containing no defective blades. This mean is equal to the total number of packets (1,00,000) multiplied by the probability of a packet containing no defective blades.

The probability of a blade being defective is given as 0.002 (or 2/1000) or 2/100 or 1/50 or 2%.

Since a packet contains 10 blades. So the probability of a packet containing no defective blades is (1 - 0.002)^10 = 0.999936 or (1-0.02)^10 = 0.99837

So the mean number of packets containing no defective blades is (1,00,000 * 0.99837) = 99837

Question 1

Substitute x in the expression

Answer:

5940

Step-by-step explanation:

495 x 12 = 5940

Answer:

B.

Step-by-step explanation:

In the attached file