Answer:
2000
Step-by-step explanation:
Since the number must be odd, it can have either 1, 3, 5, 7 or 9 in its one's place.
With a 4-digit number starting with 6, any of these digits can be in the one's place and it will still be greater than 6,000.
For the one's place, since we can choose from 5 digits, we have ⁵P₁. In the thousands place, we have one digit which is 6. For the tens and hundreds, place, we can choose from ten digits. So, we have ¹⁰P₁ and ¹⁰P₁ respectively.
So, the total number of 4 digit odd numbers greater than 6000 starting with 6 are 1 × ¹⁰P₁ × ¹⁰P₁ × ⁵P₁ = 1 × 10 × 10 × 5 = 500 numbers.
For the thousands place, we are left with the digits 7, 8 and 9. So, to arrange these 3 digits in the thousands place, we have ³P₁. For the tens and hundreds, place, we can choose from ten digits. So, we have ¹⁰P₁ and ¹⁰P₁ respectively. For the one's place, since we can choose from 5 digits, we have ⁵P₁.
So, the total number of 4 digit odd numbers greater than 6000 starting with 7, 8 or 9 are ³P₁ × ¹⁰P₁ × ¹⁰P₁ × ⁵P₁ = 3 × 10 × 10 × 5 = 1500 numbers.
So, the total number of 4-digit numbers greater than 6000 that can be constructed is 500 + 1500 = 2000 numbers.
Suzi is 1.7 meters tall. At 2:00 pm, Suzi measures her shadow to be 0.3 meters long. At the same time, a nearby tree casts a shadow that is 2.4 meters long. How tall is the tree?
Answer:
13.6 meter
Step-by-step explanation:
Given that :
Suzi's height, p1 = 1.7 m
Suzi's shadow, p2 = 0.3 m
Tree shadow, t2 = 2.4 m
Tree height, t1 =?
Using the relation :
p1 / p2 = t1 / t2
1.7 / 0.3 = t1 / 2.4
Cross multiply :
1.7 * 2.4 = 0.3 * t1
4.08 = 0.3t1
t1 = 4.08 / 0.3
t1 = 13.6
Height of the tree is 13.6 m
What is an
equation of the line that passes through the points (0,6) and (-3,2)?
Answer:
Step-by-step explanation:
y=mx+b is the general equation of a line, where
m= slope = (y2-y1)/(x2-x1)= (6-2)/(0- -3)= 4/3
b= y intercept
for point (0,6)
y=(4/3)x+b will become 6=(4/3)*0 +b, so b=6
the equation of the line that passes trough the given points is
y= (4/3) x +6
Answer:
y = 4/3 x + 6
Step-by-step explanation:
M = -4/-3 = 2/3
y = 4/3 X + B
6 = 4/3(0) + B
B=6
I NEED HELP WITH THIS ONE TOO !!
Answer:
40°
100 + 80 = 180
60 + 80 = 140
140+ 40 = 180
Step-by-step explanation:
Answer:
m<C+m<D=100 degrees m<D=40 degrees
Step-by-step explanation:
ABCD is a quadrilateral.
a) Calculate the value of x.
b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? A You must justify your answer without using a scale drawing.
Answer:
A) 45=x
B) Yes, since both A and B are 90°
6x+90=360
6x=270
x=45
No lines are not parallel
What is the inverse of the function f(x)=4x+8?
To find the inverse of a function, we switch out every x for a y and vice-versa.
Original: y = 4x + 8
Flipped: x = 4y + 8
Now, we solve for y again to put this equation into slope-intercept form.
x = 4y + 8
4y = x - 8
y = 1/4x - 2
h(x) = 1/4x - 2
Hope this helps!
Tap on the picture! Needing help ASAP please♥️
Step-by-step explanation:
everything can be found in the picture
What is the slope and y-intercept of the following equation:
= − 23 − 1
(show work pls)
Answer:
The slope is -2/3 and the y-intercept is -1.
Step-by-step explanation:
In a linear equation like this, the slope is the coefficient in front of the x after the expression has been completely simplified. In this case, the slope is -2/3.
For the y-intercept, that is simple too; since it is simplified, it is just the number that comes after the x package. So, for this, the y-intercept is -1.
Find the measure of the indicated angle to the nearest degree.
1)
A) 19°
C) 36°
B) 43°
D) 47°
Answer:
D
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan? = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{17}[/tex] , then
? = [tex]tan^{-1}[/tex] ([tex]\frac{18}{17}[/tex] ) ≈ 47° ( to the nearest degree )
nth term of an AP is given by an expression 7n-2,find the common difference of this sequence if fisrt term of sequence is 1? a.2 b.-2 c-7 d7
Step-by-step explanation:
there is something wrong with what your write here as problem description.
either there is something missing in the main expression, or in the answer options.
given your nth-term expression 7n-2, none of the 4 answer options can fit.
so, I thought, maybe there was a typo.
the possible interpretations of the expression could be
7n - 2
7(n-2)
[tex] {7}^{n} - 2[/tex]
[tex] {7}^{n - 2} [/tex]
we know that
a1 = 1
a2 = either
a1 + 2 = 3
a1 - 2 = -1
a1 + 7 = 8
a1 - 7 = -6
so, we can eliminate both negative answer options, because they would cause only negative sequence elements, but the main expression (neither of the 4 possibilities) does not allow that.
but also none of the 4 possibilities of the expression delivers any of the 4 values for a2 as described above.
7×2 - 2 = 14 - 2 = 12
7(2-2) = 7×0 = 0
7² - 2 = 49 - 2 = 47
[tex] {7}^{2 - 2} = {7}^{0} = 1[/tex]
similar not for a3.
so, if I consider your answer options right, we have 4 possible arithmetic sequences:
1. 1, 3, 5, 7, 9, 11, 13, 15, ...
2. 1, -1, -3, -5, -7, -9, -11, -13, ...
3. 1, 8, 15, 22, 29, 36, 43, 50, ...
4. 1, -6, -13, -20, -27, -34, -41, ...
the nth term expression is for
a. an = 2n - 1
b. an = 2×(-n) + 3 = 2×(-n + 1) + 1
c. an = 7n - 6
d. an = 7×(-n) + 8 = 7×(-n + 1) + 1
so, please pick the right expression from this list, and then use the answer option with the same letter.
For two complementary angles find x. The first angle is 4x+9. The second angle is 2x+27
Answer:
x = 9
Step-by-step explanation:
When sum of two angles is 90, then they are known as complementary angles.
4x + 9 + 2x + 27 = 90
4x + 2x + 9 + 27 = 90
Combine like terms
6x + 36 = 90
Subtract 36 from both sides
6x = 90 - 36
6x = 54
Divide both sides by 6
x = 54/6
x = 9
define the following key terms relating to a circle, diameter and radius
Answer:
Diameter: the straight distance from one edge of a circle to the other
Radius: the straight distance from one edge of a circle to the center
I hope this helps :)
Answer:
Diameter - a straight line that goes straight through the center of the circle to one point on its outline to another point on it's outline
Radius - a line that starts at the center and goes to anywhere on the circles circumference
$975, and there is 7 percent sales tax on the purchase.
How much is the sales tax?
Answer:
$68.25
Step-by-step explanation:
To get the sales tax, you must notice that the sales tax is 7% of 975.
That is equal to:
975 × 0.07
0.07 is equal to 7%, or [tex]\frac{7}{100}[/tex].
The answer to the equation is 68.25.
I got stuck but if someone could help me with this question it’d be greatly appreciated!
Answer:
In step 1 she multiplied the numerators together and denominators together instead she should have done this
30*5 = 12*x
150=12x
150÷12=x
12.5=x
Can someone help with 16 and 18
9514 1404 393
Answer:
16. k^5/j^3
18. 81y^20
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c) . . . . where b may be 0
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
___
We can simplify the given expressions as follows.
16.[tex]\dfrac{k^6j^2}{kj^5}=k^{6-1}j^{2-5}=k^5j^{-3}=\boxed{\dfrac{k^5}{j^3}}[/tex]
__
18.[tex](x^{-2})^2(3xy^5)^4=(x^{-2\cdot2})(3^4x^4y^{5\cdot4})=81x^{-4+4}y^{20}=\boxed{81y^{20}}[/tex]
The local library lends an average of 68.24 books to readers each day. What is the average number of books lent to readers in a week?
Answer:
Step-by-step explanation:
Set this up as a proportion and solve. The ratios are books:day, so keep in mind that a week is 7 days because your values have to be the same
[tex]\frac{books}{day}:\frac{68.24}{1}=\frac{x}{7}[/tex] and cross multiply to solve for x, the number of books lent out in a week:
x = 68.24(7) so
x = 477.68 books in a week
A box contains 3 red balls, 5 white balls, and 10 green balls. If a ball is chosen at random, what is the probability that it is either white OR green?
a. 3/10
b. 5/6
c. 1/2
d. 1/15
The correct answer is option B which is the probability of either white or green is 5/6.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
A box contains 3 red balls, 5 white balls, and 10 green balls. If a ball is chosen at random.The probability that it is either white or green will be calculated as:-
Total balls are :- 3+5+10=18
White or green ball - 5+10=15
3 x 5=15
3 x 6=18
P = N(e)/N(s) = 15/18
P = N(e)/N(s) = 5 / 6
Therefore the correct answer is option B which is the probability of either white or green is 5/6.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ2
true or false: The function f(x) = 3/x + 7x a polynomial
Answer: False
Step-by-step explanation:
If you graph this using Desmos, you can clearly see that for every x value, there are multiple y values.
A function has only one output(y) for every input(x)
True, The function f(x) = 3/x + 7x is a polynomial.
What is a polynomial?
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
The function : f(x) = 3/x + 7x
Simplifying,
f(x) = 3/x + 7x
f(x) = (3 + 7x²)/x.
And it is a polynomial with the variable x.
Therefore, it is a polynomial with the variable x.
To learn more about the Polynomials;
brainly.com/question/11536910
#SPJ2
convert decimal number system into binary number system:216
Answer:
11011000
Step-by-step explanation:
the binary equivalent of decimal number 216 is 11011000
[tex]\huge\sf\red{Answer}[/tex]
11011000
__________
Hopefully it helps
Let ABCD and EFGH be two quadrilaterals such that ABCD ~ EFGH. If AB = 15 cm, EF = 18 cm and the perimeter of ABCD is 40 cm, find the perimeter of EFGH.
Step-by-step explanation:
this photo is correct answer of this question.
HELP 20 points Congruence by SSS AND SAS NO LINKS
Answer:
where is the question oooo
helppppp and explain pls and thankyouuu
Answer:
third option (7.5, 8)
this option (6, 5, -3)
Step-by-step explanation:
you eliminate one variant by expressing it through the other(s) until you have one equation with one variable.
that you solve, and then you go back to the other elimination expressions to calculate the others.
2x - y = 7
-2x + 3y = 9
since the terms with x are already so similar, we could now simply add both equations and solve that result :
2x + (-2x) -y + 3y = 7+9 = 16
0×x + 2y = 16
2y = 16
y = 8
=>
2x - 8 = 7
2x = 15
x = 7.5
x - 2y - 3z = 5
x + 2y + 3z = 7
x + z = 3
the same trick by adding the first 2 equations
x + x -2y + 2y -3z + 3z = 5 + 7 = 12
2x + 0y + 0z = 12
2x = 12
x = 6
=>
6 + z = 3
z = -3
and then
6 + 2y + 3(-3) = 7
6 + 2y - 9 = 7
2y - 3 = 7
2y = 10
y = 5
What is the area, in square inches, of the trapezoid below
Answer:
89.2 in^2
Step-by-step explanation:
1/2(15.7+6.6)(8)
=89.2 in^2
Answer:
A = 89.2 in²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 8, b₁ = 6.6, b₂ = 15.7 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (6.6 + 15.7) = 4 × 22.3 = 89.2 in²
A committee that consists of five members are to be chosen from 6 boys and 5 girls. Find the number of different committees that can be formed if the number of boys is more than the number of girls
Answer:
281 different committees can be formed if the number of boys is more than the number of girls.
Step-by-step explanation:
The order in which the people are chosen to the committee is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Number of boys more than the number of girls:
3, 4 or 5 boys.
3 boys:
3 boys from a set of 6.
2 girls from a set of 5. So
[tex]C_{6,3}C_{5,2} = \frac{6!}{3!3!} \times \frac{5!}{2!3!} = 200[/tex]
4 boys:
4 boys from a set of 6.
1 girl from a set of 5. So
[tex]C_{6,4}C_{5,1} = \frac{6!}{4!2!} \times \frac{5!}{1!4!} = 75[/tex]
5 boys:
5 boys from a set of 6. So
[tex]C_{6,5} = \frac{6!}{5!1!} = 6[/tex]
Total:
200 + 75 + 6 = 281
281 different committees can be formed if the number of boys is more than the number of girls.
What is the variable expression for 6 less than the difference of 5 and a number? * 3 points 6 - 5 - n 6 - n - 5 (5 - n) -6 6 - (5 - n)
Given:
The given statement is "6 less than the difference of 5 and a number".
To find:
The variable expression for the given statement.
Solution:
Let n be the unknown number or the variable.
We know that minus sign is used to represent the difference between two numbers.
Difference of 5 and a number is [tex](5-n)[/tex].
6 less than the difference of 5 and a number is [tex](5-n)-6[/tex].
The required expression for the given statement is [tex](5-n)-6[/tex].
Therefore, the correct option is C.
Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school.
Anna draws a map with a number line connecting her house to Ben’s house. On the number line, the school is at 0 and her house is at the point +2.5. On the map, Ben’s house is at the point
Answer:
Step-by-step explanation:
3===o===2=======1========0========-1=======x-2
I know this is backwards, but the question makes the choice of which direction is plus. o represents where anna lives.
Ben should be right at -2 where the x is.
In 25 words or fewer, is this solution reasonable? Why or why not?
Step-by-step explanation:
This solution is reasonable because equal slopes are parallel and negative reciprocals are perpendicular. Four right angles make up a rectangle, and this fulfills it
brainlest if correct !!!!!
Answer: C. x > 0
Step-by-step explanation:
It is an empty circle, meaning the value of 0 is not included in the inequality, so it's not ≤ or ≥.The arrow goes to the right, towards values greater than 0, therefore it is > and not <.The answer would be x > 0.
Answer:
C
Step-by-step explanation:
There are 25 employees in a office.22 have cell phones 19 have cars, and 2 have niether. How many employees have both.
Answer:
18
Step-by-step explanation:
Let the number of employees with both cell and car be b. Using a Venn diagram shown above,
19 + 22 - b + 2 = 25
43 - b = 25
b = 18
In rectangle ABCD, AC = 48 andBO = 5x + 4. What's the value of x?
8.8
4
8
9
Helppppp and explain thankyouuuu
Answer:
whats the question sir
Step-by-step explanation:
can you show me it like type it for me