Solve the logarithmic equation. write the answer in exact, simplified form. log(-c) + log8= log (7c-75)

Step-by-step explanation:

Let S be the set of all the stores in the sample, A be the set of stores dealing with Asian companies and E but the set of stores dealing with European companies

i. The set of stores that deal with European or Asian companies is A ∪ E. The inclusion-exclusion principle states that |A ∪ E| = |A| + |E| - |A ∩ E| = 266 + 308 - 103 = 471. So P(A ∪ E) = 471/500 = 0.942

ii. E' = S - E. |S-E| = 500 - 308 = 192. So P(E') = 192/500 = 0.384

iii. |A - E| = |A| - |A ∩ E| = 266 - 103 = 163. So P(A - E) = 163/500 = 0.326

iv. Stores that do not deal with only one type of company, must deal with both Asian and European companies. We are given that |A ∩ E| = 103. So P(A ∩ E) = 103/500 = 0.206

Easy, right?

Then mark as brainlist!

Answer:

Step-by-step explanation:

Distance around = 2*160 + 2*360

= 320 + 720

= 1080 feet.

The distance around the field is 1040 feet.

It is required to find the distance around the field.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

A football field is 160 feet wide and 360 feet in length.

A  football field is in the shape of rectangle.

So, we know that ,

Perimeter of rectangle= 2(length +breadth)

Distance around

= 2(160 + 360)

=2(520)

= 1040 feet.

Hence,  the distance around the field is 1040 feet.

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Answer:

29 years

Step-by-step explanation:

[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]

From here I'll just use a calculator & get 28.7, or 29 years.

Answer:

force = work/distance

force = 900/5

force = 180 N

An equivalent ratio of the given ratio 6/7 is; 12/14

To find equivalent ratios, we will just multiply the given ratio by any number that is equivalent to 1 such as 2/2, 3/3, 4/4, 5/5 e.t.c

Now, we want to find equivalent ratio of 6/7. Applying the procedure above, we can say that;

Equivalent ratio = (6/7) * (2/2) = 12/14

Thus, an equivalent ratio of 6/7 is; 12/14

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Dwayne will drink 12 bottles of water in 4 days.

To find out how many bottles of water Dwayne will drink in 4 days, we can set up a proportion based on the information given:

Let x be the number of bottles of water he will drink in 4 days.

The number of bottles of water consumed per day remains constant, so we can set up the following proportion:

48 bottles / 12 days = x bottles / 4 days

Now, solve for x:

48 / 12 = x / 4

4x = 48

x = 48 / 4

x = 12

So, Dwayne will drink 12 bottles of water in 4 days.

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The angle m∠ABC is 70 degrees.

The angle in a rhombus can be found as follows;

The opposite angle of a rhombus are congruent.

Therefore,

∠B = 140 degrees

Hence, the diagonal of a rhombus bisect an angle.

Therefore,

m∠ABC = 140 / 2

m∠ABC = 70 degrees.

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The linear equation for the cost that the household spend in water is given by:

C(d) = 237d + 1200.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the free usage of 1200 liters is the y-intercept, while the daily usage of 237 liters is slope. Hence the function for the amount the household spends in water in d days is given as follows:

C(d) = 237d + 1200.

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Answer:

1.D 2.C 3.A 4.B

Step-by-step explanation:

hope this helped

Answer:

C. 4^6 / 5^6

Step-by-step explanation:

(4/5)^6

= 4^6 / 5^6

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]

[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]

[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]

[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]

[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]

[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 1. an = n + 4,   2. ( 3 1/2, 3.5, 5),   3. 6 1/12,   4. 97,   5. 0.2 meters,    6. 4.52,   7. 3 1/18

Step-by-step explanation:

Answer:

13. 10a^4b²

14. -5y³ + 35y² - 10y

Step-by-step explanation:

Question 13:

(5a³b) (2ab) =

=10a^4b²

Question 14:

5y (-y² + 7y - 2) =

= -5y³ + 35y² - 10y

Hope this helps!

It should be noted that mathematical transformations involve changing an image in some prescribed manner.

Your information is incomplete. An overview will be given. A transformation is a general term for the specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

It should be noted that the original shape of the object is called the pre-Image and the final shape and position of the object is the image under the transformation.

There are four main types of transformations: translation, rotation, reflection and dilation. Also, in geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other

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Answer:

1. a translation and reflection

2. only rigid transfotmations

3. are congruent

Step-by-step explanation:

right on edmentum

Answer: Reflection across x=2.

Step-by-step explanation:

x=2 is the perpendicular bisector of segment UU'.

The volume of the given composite figure is: 375 m³.

Volume of the composite figure = volume of triangular prism at the bottom + volume of rectangular prism at the top.

Volume of the composite figure = 0.5 * b * h * length + (l)(h)(w)

= 0.5 * 5 * 4 * 5 + (13)(5)(5)

= 50 + 325

Volume of the composite figure = 375 m³

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The correct option is D: G(x) = -5x².

The equation of G(x) will be -5x² after vertically stretching and flipping.

A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.

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The complete question is -

The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?

A: G(x) = -1/5x²

B: G(x) = 5x²

C: G(x) = 1/5x²

D: G(x) = -5x²

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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A parallelogram is a type of quadrilateral that has opposite sides to be equal, and opposite angles to be equal.

Thus to complete the given proof in the question, the required statements and reasons are stated below:

             STATEMENT                                     REASONS

1. AB ≅ CD,                                                    Opposite sides of a

  BC ≅ AD                                                      parallelogram are equal

2. A, B, C, and D form a paralelogram         Given

3. Draw AC and BD                                       Drawing line segments

4. AB = CD,                                                    Equal line segments have

   BC = AD                                                     equal measures

5. ΔABC ≅ ΔCDA                                         SSS criterion for equal

   ΔABD ≅ ΔCDB                                         triangles

6. <BAD ≅ <DCB                                          Corresponding angles of equal

   <ABC ≅  <CDA                                         triangles are equal    

7. AC = AC, and BD = BD                             Reflective property of equality

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Answer:

98 days

Step-by-step explanation:

140*70%=140*(7/10)=14*7=98

Answer:

16

Step-by-step explanation:

The student uses the ratio of 4 oranges to 6 fluid ounces.

When there are 24 fluid ounces, the number of oranges will be:

= 4/6 × 24

= 16 oranges

Answer:

10 years old

Step-by-step explanation:

Let m = mother's age

Let f = father's age

Let d = Dina's age

m = 4d               d = f-35                f = m+5

Substitute the middle equation in to the first equation

m = 4(f - 35) Use the distributive property

m = 4f - 140 subtract 4f from both sides

*m -4f = -140

In equation 3 above, subtract m from both sides  to get

f = m+5

f - m = 5  rearrange so that the  m term is first

*-m + f = 5  

Now add the equations together that have *

m -4f = -140

-m + f = 5

     -3f = -135  Divide both sides by -3

f = 45  This is the father's age.  To find Dina's age, plug 45 into the second equation above:

d = f -35

d = 45 -35

d = 10.

To find the mom's age, use the third equation:

f = m+5

45 = m + 5

40 = m

You can check this by plugging the answers you found and you can see that all three equations are solved.

m = 4d                        d = f - 35                 f = m + 5

40 = 4(10)                    10 = 45 - 35            45 = 40 + 5

40 = 40                       10 = 10                     45 = 45

Calculating the circumference of a circle based on the circle's diameter.

What kind of problems can a quantum computer solve?

10 Difficult Problems Quantum Computers can Solve Easily-

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The complete question is -

Which type of mathematical problem is too complex for a classical computer to solve efficiently?

a. converting an irregular fraction to an approximate decimal value

b. multiplying two numbers that both have a large number of digits

c. finding two prime factors that result in a specific value when multiplied

d. calculating the circumference of a circle based on the circle's diameter

Hi! ❄

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

The rule for this sequence is 'multiply by -6'.

Verification ↓

-3*(-6)[tex]\stackrel\checkmark{=}[/tex]18

18*(-6)[tex]\stackrel\checkmark{=}[/tex]-108

So the rule for the sequence is 'multiply by -6'

And the Common ratio is -6.

Hope that made sense !!

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

[tex]\star\tiny\pmb{calligraphy}\star[/tex]

[tex]\textbf{Heya !}[/tex]

✏✏[tex]\large\textsf{Given:-}[/tex]

✏✏ [tex]\large\textsf{To Find:-}}[/tex]

✏✏ [tex]\large\textsf{Solution Steps:-}[/tex]

What do we multiply each term of the sequence by to arrive at the next one ? we can find that by dividing the last term of the sequence, -108, by the middle term, 18:-

[tex]\large{\sf{\longmapsto{-108\div18=-6}[/tex]

Now divide 18 by the first term (-3) :-

[tex]\longmapsto\sf{18\div-3=-6}[/tex]

we arrived at -6 twice, So the rule for this sequence is:- "Multiply by -6, And you'll arrive at the next term"

`hope it helped ~ :D

Answer:

26.

Step-by-step explanation:

(11+14+23+16+x) / 5 = 18   where x is the value to be added.

(64 + x) / 5 = 18

64 + x = 90

x = 90 - 64

  =  26.

Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.

As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2, R_1 > R_2[/tex], the ratio of the intensities is given by:

[tex]R = 10^{\frac{R_1}{R_2}}[/tex]

For this problem, the intensities are:

[tex]R_1 = 7.8, R_2 = 5.6[/tex]

Hence the ratio is:

[tex]R = 10^{\frac{7.8}{5.6}} = 24.71[/tex]

The San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.

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The a28th term of a arithmetic sequence is -242.

According to the statement

We have given that :

a1 = 1 and d = -9. And by use of it we have to find the value of the a28th term in the arithmetic sequence.

So, arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

And the formula is

an = a1 +(n-1)d

here put the values in it

an = a28 , n = 28, d =-9, a1 =1

then

an = a1 +(n-1)d

a28 = 1 +(28-1)(-9)

a28 = 1 +(27)(-9)

a28 = 1 -243

a28 = -242.

So, The a28th term of a arithmetic sequence is -242.

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The given center and point on the circle of (0,0) and (-5, 3), respectively

gives the equation of the circle as [tex]x^{2} +y^{2} =\sqrt{34}[/tex].

The general form of the equation of the circle is presented as follows

(x - h)² + (y - k)² = r²

Where,(h, k) is the center of the circle and r is the radius of the circle

Here (h, k) is centered about the origin and the radius of the circle

Radius of the circle = √[(-5-0)² + (3-0)²]

= √(25+9)

=√34.

The equation of a circle centered on the origin going through the point (-5,3)

[tex]x^{2} +y^{2} =\sqrt{34}[/tex]

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Answer:

A=120

B=165

C=240

Step-by-step explanation:

The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

According to the statement

we have given the statement and we have to show that the statement is a true or false after analyzing.

So, to analyse the statement

Context diagrams show the interactions between a system and other actors (external factors) with which the system is designed to interface. System context diagrams can be helpful in understanding the context .

But we know that the standardized names is not used within each set of symbols. so, this is used in a randomly sets.

that's why the given statement is not true in the case of the standardized names.

So, The statement is False that When drawing a context diagram, standardized names should be used within each set of symbols.

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x would be the side-length of a square that has the same area as a rectangle with width b and length a.

√(a*b) = x

Notice that you have two "lengths" which are a and b.

And you want to find x such that:

a/x = x/b

Now, notice that w e can rewrite the above expressions as:

a*b  = x*x

This means that x would be the side-length of a square that has the same area as a rectangle with width b and length a.

Now, if you know the values of a and b (you can get these by using a ruler for example)

Then you can replace them in the equation:

a*b = x*x

√(a*b) = x

And find the value of x that meets the given condition.

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