Answer:
[tex]=1-log\left(1432590\right)[/tex]Step-by-step explanation:
By the logarithm properties:
[tex]\begin{gathered} \log_(a*b)=\log_a+logb \\ \log_(\frac{a}{b})=\text{ log a - log b} \\ \log_(a^b)=b\log_a \end{gathered}[/tex]Therefore, for the given logarithm:
[tex]\begin{gathered} 1-(log510+log53^2) \\ =1-(log510+log2809) \\ =1-log\left(1432590\right) \end{gathered}[/tex]i need help who know how to do this ?
The total amount needed for the equipment is $350.
The number of students on the team is x students.
To find the amount required per student, consider that each student will pay equally. Therefore, the amount can be gotten by division.
Hence, the amount per student can be gotten as:
[tex]\Rightarrow\frac{\text{Amount}}{\text{Number of Students}}[/tex]This then becomes, by substitution:
[tex]=\frac{350}{x}[/tex]The correct answer is OPTION C.
Complete the word problem and show the work for each section
(G.11b, 1 point) Two chords intersect with the measures shown in the drawing. What is the value of x? 5 6.5 8 O A. 2.2 O B. 6.2 0 C. 8.0 OD. 13.5
The value of x is 6.2
Here, we want to find the value of x
To do this, we use the theorem of intersecting chords
By this theorem, the products of the two sides of two chords which intersects are the same
Mathematically, we have this as follows;
[tex]\begin{gathered} 5\text{ }\times\text{ 8 = 6.5 }\times\text{ x} \\ \\ 40\text{ = 6.5x} \\ \\ x\text{ = }\frac{40}{6.5} \\ \\ x\text{ = 6.15 which is approx. 6.2} \end{gathered}[/tex]the table shows the number of people p(t), register for a conference t days after registration opens. which function best approximates the data?
The function which aproximates better the data is:
[tex]P(t)=20(2^t)[/tex]because:
[tex]P(0)=20[/tex][tex]P(1)=20(2)=40[/tex][tex]P(2)=20(2^2)=80[/tex][tex]P(3)=20(2^3)=20(8)=160[/tex][tex]P(4)=20(2^4)=20(16)=320[/tex]What does b equal to in this equation 88 = x(0) + b?
answer: b= 88
CalculatorIn the coordinate plane, what is the length of the line segment that connects points at (4, -1) and (9, 7)?Enter your answer in the box. Round to the nearest hundredth.units1 2 3 45 6 7 8
The formula to calculate the distance between two points is given by
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]In this problem, we have the coordinates
(4, -1) and (9, 7)
substitute in the formula
[tex]\begin{gathered} d=\sqrt{(7+1)^2+(9-4)^2} \\ d=\sqrt{8^2+5^2} \\ d=\sqrt{89} \\ d=9.43 \end{gathered}[/tex]The answer is 9.43 unitsJack is making a scale drawing of his house. He has decided to use a scale of 1 in.: 100 m. If a part of his house is 20 m long, what will be the length of this part on his scale drawing?
we can use cross-multiplication
[tex]\begin{gathered} 1\longrightarrow100 \\ x\longrightarrow20 \end{gathered}[/tex]where x is the measure we need
[tex]\begin{gathered} x=\frac{20\times1}{100} \\ x=0.2 \end{gathered}[/tex]so, the measure is 0.2 in
5. Graph y = -12x - 61 + 1 + 361
We have to graph the function:
[tex]f(x)=-|2x-6|+1[/tex]To do that we can start by looking at which point the absolute function changes direction.
This happens when 2x-6=0.
[tex]\begin{gathered} 2x-6=0 \\ 2x=6 \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]We have one line for x<3 and other line, with different slope, for x>3.
Then we define the function as a piecewise function:
For x<3, we have:
[tex]\begin{gathered} x<3\longrightarrow2x-6<0\longrightarrow|2x-6|=-(2x-6) \\ f(x)=-(-(2x-6))+1 \\ f(x)=2x-6+1 \\ f(x)=2x-5 \end{gathered}[/tex]And for x>3:
[tex]\begin{gathered} x>3\longrightarrow2x-6>0\longrightarrow|2x-6|=2x-6 \\ f(x)=-(2x-6)+1 \\ f(x)=-2x+6+1 \\ f(x)=-2x+7 \end{gathered}[/tex]We can resume the function f(x) as:
[tex]f(x)=\begin{cases}2x-5;x<3 \\ -2x+7\colon x\ge3\end{cases}[/tex]For x<3, we have a positive-slope line (m=2), with y-intercept b=-5.
For x>3, we have a negative-slope line (m=-2), with y-intercept b=7 (but as x>3, the y-axis is not intercepted by this line). We also can use the reference that, when x=3, y=1.
We can graph this as:
NOTE: I draw them with different colours for each part of the function, but it is the same function and should be drawn with the same colour.
Select the interval (6,100) as an inequality and using set notation.
We are given the following interval:
(6,100].
This means that we want values greater than 6(since the interval is open at 6 it is not part of the interval) and lesser than or equal to 100(since the interval is closed at 100 it is part of the interval).
Inequality:
Greater than 6 and lesser than or equal to 100 is represented by the following inequality:
[tex]6Set notation:Similar to the inequality, just with a prior notation.
[tex]\left\lbrace x\right|6Write an equation that represents each side of the figure.please help as soon as possible.
EXPLANATION:
The correct equation is the one formulated below since we can see that two of its sides have the same measure, therefore, looking at the coordinates well, we have the following formula.
EQUATION:
[tex]\begin{gathered} 5x^2-1y^2^{} \\ \end{gathered}[/tex]Find all solutions to the equation 4ln(5x)+5=2. Show your work.
Given the equation:
[tex]4\ln \mleft(5x\mright)+5=2[/tex]We will find the value of (x) as follows:
a) subtract 5 from both sides
[tex]\begin{gathered} 4\ln \mleft(5x\mright)+5-5=2-5 \\ 4\ln \mleft(5x\mright)=-3 \end{gathered}[/tex]b) Divide both sides by 4
[tex]\ln (5x)=-\frac{3}{4}[/tex]c) Taking the exponential of both sides to remove ln
[tex]5x=e^{-\frac{3}{4}}[/tex]Finally, divide both sides by 5
[tex]x=\frac{1}{5}e^{-\frac{3}{4}}\approx0.09447[/tex]So, the answer will be x = 0.09447
A gas tank of a car has a volume of 72.4 dm3. Find how many kiloliters of gas it would take to completely fill the gas tank.
Given:
Volume = 72.4 dm³
Hence:
[tex]72.4\text{ }dm^3\times\frac{1kL}{1000\text{ }dm^3}[/tex]ANSWER
0.0724 kL, would completely fill the gas tank.
how many solutions does y=2x^2-3x+5
When we have a polynomial, the amount of solutions for a polynomial is given by its degree, and the degree of the polynomial is given by the biggest exponent in the polynomial. Our polynomial is
[tex]y=2x^2-3x+5[/tex]The biggest exponent is 2, therefore this is a 2nd degree polynomial. This means this polynomial has 2 solutions.
For babies between 1 and 11 months old, the equation y=1.2x + 8.9 models the baby's weight when the baby is x months old. What is the meaning of the slope in the context of this situation?
For a equation of the form:
[tex]y=mx+b[/tex]y = dependent variable = baby's weight
x = Independent variable = Number of months
b = y-intercept =Initial weight of the bay
m = Slope = rate of change = 1.2
In this sense, the answer is:
For everything increase of 1 month, the baby's weight increases by 1.2 lb
The country of Whoville has export sales of $9 billion, government purchases of $1,022 billion, business investment is $42 billion, imports are $28 billion, and consumption spending is $1,945 billion. What is the value of GDP in billions of dollars?
Answer
The GDP of Whoville is $2990 billion
Step-by-step explanation:
The formula for calculating GDP is given as
GDP = C + G + I + NX
Where, C = all private consumption
G = All government spending
I = Investment by businesses
NX = The country's net export
The net export = total export - total import
Total export = $9 billion
Total import = $28 billion
The net export = ($9 - $28) billion
The net export = - $19 billion
GDP = [($1945 + $1022 + $42 + (- $19)] billion
GDP = ($1945 + $1022 + $42 - $19)
GDP = $2990 billion
Hence, the GDP of Whoville is $2990 billion
Identify the constant difference for a hyperbole with foci (-3, 0) and (3, 0) and a point on the hyperbola (7, 0)A. 14B. 6C. 10D. 2
Let the coordinates of the focus(-3, 0) be:
x₁ = -3, y₁ = 0
Let the coordinates of the focus(3, 0) be:
x₂ = 3, y ₂ = 0
Let the coordinates of point(7, 0) be:
x₃ = 7, y₃ = 0
Let the distance between the Focus(-3, 0) and (7, 0) be d₁
[tex]\begin{gathered} d_1=\text{ }\sqrt[]{(x_3-x_1)^2+(y_3-y_1)^2} \\ d_1=\text{ }\sqrt[]{(7-(-3))^2+(0-0)^2} \\ d_1=\text{ }\sqrt[]{10^2} \\ d_1=\text{ 10} \end{gathered}[/tex]Let the distance between the Focus (3, 0) and (7, 0) be d₂
[tex]undefined[/tex]I am really struggling and if anyone can help with these problems it would mean the world I need to get them done and I need to be eligible for sports please and thank you a lot solve question number 1
Explanation
The area and circumference of a circle can be seen below.
[tex]\begin{gathered} \text{Area}=\pi r^2 \\ \text{Circumference}=2\pi r \end{gathered}[/tex]From the image, the diameter of the circle is given as;
[tex]d=16.6m[/tex]Recall;
[tex]\text{radius(r)}=\frac{\text{diameter}}{2}=\frac{16.6}{2}=8.3m[/tex]Hence;
[tex]\begin{gathered} \text{Area}=\pi\times8.3^2=216.4m \\ \text{Circumference = 2}\times\pi\times8.3=52.2m \end{gathered}[/tex]Answer:
[tex]\begin{gathered} A=216.4m \\ C=52.2m \end{gathered}[/tex]Find one positive AND one negative angle that are co-terminal with the given angle.π/3Be sure to label and leave your answers in radians (not degrees).
One positive angle:
[tex]\frac{\pi}{3}+2\pi=\frac{7\pi}{3}[/tex]One negative angle:
[tex]\frac{\pi}{3}-2\pi=-\frac{5\pi}{3}[/tex]Solve 19x-9 ≥ - 1 + 6x
In order to solve this inequality, let's put all terms with x on the same side of the inequality, add the like terms and divide both sides by the coefficient of x.
So we have:
[tex]\begin{gathered} 19x-9\ge-1+6x \\ 19x-6x\ge-1+9 \\ 13x\ge8 \\ x\ge\frac{8}{13} \end{gathered}[/tex]Therefore the solution is x >= 8/13
Sarah started a stamp collection with 12 stamps. She will buy 75 stamps each monthfor a certain number of months to add to her collection. After how many months willSarah have at least 200 stamps?
initial stamps = 12
Stamps bought per month = 75
number of moths = x
So the expression for the total number of stamps(y)
y =12+75x
To have 200 stamps replace y by 200 and solve for x (months)
200 = 12+75x
200-12 = 75x
188 =75x
188/75 =x
2.5 = months
2.5 months (2 and a half)
My phone went dead I am plugged back in now I need to know how to fix this problem out
We have that
[tex]8\times10^8=800000000[/tex]So the answer is the first one.
how would I solve this problem with synthetic division and graph it without a calculator?
List the factors for 60
In order to find the factors of 60, let's divide it by the prime numbers, starting with 2, as many times we can, until we reach 1:
[tex]\begin{gathered} 60/2=30 \\ 30/2=15 \end{gathered}[/tex]15 can't be divided by 2, so we can continue with 3:
[tex]15/3=5[/tex]5 is already a prime number, so it can only be divided by itself:
[tex]5/5=1[/tex]Now, to find all factors, let's multiply the prime factors by themselves:
[tex]\begin{gathered} \text{prime factors: 2, 2, 3, 5} \\ 2\cdot2=4 \\ 2\cdot3=6 \\ 2\cdot5=10 \\ 2\cdot2\cdot3=12 \\ 3\cdot5=15 \\ 2\cdot2\cdot5=20 \\ 2\cdot3\cdot5=30 \end{gathered}[/tex]Therefore the factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 99% confidence that the sample mean is within $4 of the population mean, and the population standard deviation is known to be $75
ANSWER:
2333 students
STEP-BY-STEP EXPLANATION:
Given:
Margin of error (E): 4
Standard deviation (σ): 75
Confidence level (CI): 99%
For this confidence level the value of z is equal to 2.576.
We can calculate the necessary sample size with the following formula:
[tex]E=z\cdot\left(\frac{\sigma}{\sqrt{n}}\right)[/tex]Substituting each value we calculate the value of n, like this:
[tex]\begin{gathered} 4=2.576\cdot \left(\frac{75}{\sqrt{n}}\right) \\ \\ \frac{75}{\sqrt{n}}=\frac{4}{2.576} \\ \\ \sqrt{n}=\frac{75\cdot2.576}{4} \\ \\ n=\left(\frac{75\cdot2.576}{4}\right)^2 \\ \\ n=2332.89\cong2333 \end{gathered}[/tex]The number of students to be selected must be 2333
I need help with a question
k is the midpoint of JL
KL= 7n+ 10
JL= 76
Since k is the midpoint, then;
JK = KL = 7n + 10
Also
JL = JK + kL
76 = (7n + 10) + (7n+10)
76 = 7n + 10 + 7n + 10
76 = 14n + 20
subtract 20 from both-side of the equation
76 - 20 = 14n
56 = 14n
divide both-side of the equation by 14
56/14 = n
4 = n
n = 4
JK= 7n + 10 = 7(4) + 10 = 28 + 10 = 38
KL=JK=38
KL=38
6. Which point is the midpoint of AE?1BСE8 7 6 5 4 3 2 1 01234S678A. CB. BC. not B, C, or DD. D
we have that
the x-coordinate of A is -6
the x-coordinate of E is 6
so
the midpoint of AE is
(-6+6)/2=0
therefore
the midpoint is point C
answer is option Aare each of those congruent and if so what is there postulate
ANSWERS
a. Yes, congruent. By SSS postulate
b. Yes, congruent. By AAA postulate
c. Yes, conguent. By SAS postulate
EXPLANATION
a. Sides MQ and MN are congruent as shown in the diagram. So are sides PN and PQ. Side PM is shared by both triangles so it must be congruent to both.
b. It is shown in the diagram which angles are congruent:
c. Angles DEC and AEB are vertical angles and they are therefore congruent. The two sides that form those angles are shown congruent in the diagram, so we have a side, the next angle and the next side: SAS postulate.
(4x2 – 2x + 1) – (5x2 – 7x - 5 )
,We have the next expression
[tex](4x^2-2x+1)-(5x^2-7x-5)[/tex]First we will multiplicate the sign minus with the trinomial (5x^2 – 7x - 5 )
[tex]4x^2-2x+1-5x^2+7x+5[/tex]then we can sum like terms and we obtain the solution
[tex]-x^2+5x+6[/tex]Write the equation in slope-intercept form and then graph the equation that passes through (-4, -1) and is parallel to to y = −1/2x + 1
The general slope-intercept form of a linear equation is:
[tex]y=mx+b[/tex]----------------------------------------
You have a linear equation parallel to:
[tex]y=-\frac{1}{2}x+1[/tex]That means that both equations have the same slope
m= - 1/2
If the equation passes through (-4 , -1) we can use that point to find the value of the b in the slope-intercept form:
(-4 , -1) x= - 4 y= - 1
[tex]-1=-\frac{1}{2}(-4)+b[/tex]We clear the b:
[tex]-1=\frac{4}{2}+b[/tex][tex]-1=2+b[/tex]Then you know the values of
m=-1/2
b=-3
The equation in slope-intercept form is:
[tex]y=-\frac{1}{2}x-3[/tex]To graph a linear equation you need two point, as you have (-4, -1) and the point of the y-intercept that is (0,b) = (0,-3)
You put in the plane the two points:
And you draw a line that link the two points to get the final graph:
Do not round any intermediate computation, and round your final answer to the nearest cent.
SOLUTION:
Case: Simple interest
Method:
P= $5100
R= 6.5% or 0.065 annual rate
T= 365 days.
1. The formula for simple Interest is:
[tex]I=PRT[/tex]Therefore:
[tex]\begin{gathered} I=5100\times0.065\times\frac{365}{365} \\ I=331.50 \end{gathered}[/tex]The Interest, I= $331.50
2. The Amount, A
[tex]\begin{gathered} A=P+I \\ A=5100+331.50 \\ A=5431.50 \end{gathered}[/tex]The Amount A= $5431.50